Book Review
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3090423
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Book Information:
Authors:
Dorian Goldfeld and
Joseph Hundley
Title:
Automorphic representations and L-functions for the general linear group. Volume I
Additional book information:
Cambridge Studies in Advanced Mathematics, Vol. 129,
Cambridge University Press,
Cambridge,
2011,
xx+550 pp.,
ISBN 978-0-521-47423-8,
US $105.00
Authors:
Dorian Goldfeld and
Joseph Hundley
Title:
Automorphic representations and L-functions for the general linear group. Volume II
Additional book information:
Cambridge Studies in Advanced Mathematics, Vol. 130,
Cambridge University Press,
Cambridge,
2011,
xx+188 pp.,
ISBN 978-1-107-00794-4,
US $82.00
James Arthur, The work of Ngô Bao Châu, Proceedings of the International Congress of Mathematicians. Volume I, Hindustan Book Agency, New Delhi, 2010, pp. 57–70. MR 2827882
James Arthur and Laurent Clozel, Simple algebras, base change, and the advanced theory of the trace formula, Annals of Mathematics Studies, vol. 120, Princeton University Press, Princeton, NJ, 1989. MR 1007299
Emil Artin and John Tate, Class field theory, AMS Chelsea Publishing, Providence, RI, 2009. Reprinted with corrections from the 1967 original. MR 2467155, DOI 10.1090/chel/366
Mahdi Asgari and Freydoon Shahidi, Generic transfer for general spin groups, Duke Math. J. 132 (2006), no. 1, 137–190. MR 2219256, DOI 10.1215/S0012-7094-06-13214-3
Mahdi Asgari and Freydoon Shahidi, Generic transfer from $\rm GSp(4)$ to $\rm GL(4)$, Compos. Math. 142 (2006), no. 3, 541–550. MR 2231191, DOI 10.1112/S0010437X06001904
A. Borel, Automorphic $L$-functions, Automorphic forms, representations and $L$-functions (Proc. Sympos. Pure Math., Oregon State Univ., Corvallis, Ore., 1977) Proc. Sympos. Pure Math., XXXIII, Amer. Math. Soc., Providence, R.I., 1979, pp. 27–61. MR 546608
Armand Borel and W. Casselman (eds.), Automorphic forms, representations and $L$-functions. Part 1, Proceedings of Symposia in Pure Mathematics, XXXIII, American Mathematical Society, Providence, R.I., 1979. MR 546586
Armand Borel and W. Casselman (eds.), Automorphic forms, representations, and $L$-functions. Part 2, Proceedings of Symposia in Pure Mathematics, XXXIII, American Mathematical Society, Providence, R.I., 1979. MR 546606
Armand Borel and George D. Mostow (eds.), Proceedings of Symposia in Pure Mathematics. Vol. IX: Algebraic groups and discontinuous subgroups, American Mathematical Society, Providence, R.I., 1966. MR 0202512
Christophe Breuil, Brian Conrad, Fred Diamond, and Richard Taylor, On the modularity of elliptic curves over $\mathbf Q$: wild 3-adic exercises, J. Amer. Math. Soc. 14 (2001), no. 4, 843–939. MR 1839918, DOI 10.1090/S0894-0347-01-00370-8
D. Bump, J. W. Cogdell, E. de Shalit, D. Gaitsgory, E. Kowalski, and S. S. Kudla, An introduction to the Langlands program, Birkhäuser Boston, Inc., Boston, MA, 2003. Lectures presented at the Hebrew University of Jerusalem, Jerusalem, March 12–16, 2001; Edited by Joseph Bernstein and Stephen Gelbart. MR 1990371
Daniel Bump, The Rankin-Selberg method: a survey, Number theory, trace formulas and discrete groups (Oslo, 1987) Academic Press, Boston, MA, 1989, pp. 49–109. MR 993311
Daniel Bump, Automorphic forms and representations, Cambridge Studies in Advanced Mathematics, vol. 55, Cambridge University Press, Cambridge, 1997. MR 1431508, DOI 10.1017/CBO9780511609572
Daniel Bump, The Rankin-Selberg method: an introduction and survey, Automorphic representations, $L$-functions and applications: progress and prospects, Ohio State Univ. Math. Res. Inst. Publ., vol. 11, de Gruyter, Berlin, 2005, pp. 41–73. MR 2192819, DOI 10.1515/9783110892703.41
William Casselman, Introduction to the representation theory of $p$-adic groups, http://www. math.ubc.ca/~cass/research/pdf/p-adic-book.pdf.
Laurent Clozel, Michael Harris, and Richard Taylor, Automorphy for some $l$-adic lifts of automorphic mod $l$ Galois representations, Publ. Math. Inst. Hautes Études Sci. 108 (2008), 1–181. With Appendix A, summarizing unpublished work of Russ Mann, and Appendix B by Marie-France Vignéras. MR 2470687, DOI 10.1007/s10240-008-0016-1
J. W. Cogdell, Dual groups and Langlands functoriality, An introduction to the Langlands program (Jerusalem, 2001) Birkhäuser Boston, Boston, MA, 2003, pp. 251–268. MR 1990382
J. W. Cogdell, H. H. Kim, I. I. Piatetski-Shapiro, and F. Shahidi, On lifting from classical groups to $\textrm {GL}_N$, Publ. Math. Inst. Hautes Études Sci. 93 (2001), 5–30. MR 1863734, DOI 10.1007/s10240-001-8187-z
J. W. Cogdell, H. H. Kim, I. I. Piatetski-Shapiro, and F. Shahidi, Functoriality for the classical groups, Publ. Math. Inst. Hautes Études Sci. 99 (2004), 163–233. MR 2075885, DOI 10.1007/s10240-004-0020-z
J. W. Cogdell and I. I. Piatetski-Shapiro, Converse theorems for $\textrm {GL}_n$, Inst. Hautes Études Sci. Publ. Math. 79 (1994), 157–214. MR 1307299
J. W. Cogdell and I. I. Piatetski-Shapiro, Converse theorems for $\textrm {GL}_n$. II, J. Reine Angew. Math. 507 (1999), 165–188. MR 1670207, DOI 10.1515/crll.1999.507.165
James W. Cogdell, $L$-functions and converse theorems for $\textrm {GL}_n$, Automorphic forms and applications, IAS/Park City Math. Ser., vol. 12, Amer. Math. Soc., Providence, RI, 2007, pp. 97–177. MR 2331345, DOI 10.1090/pcms/012/04
James W. Cogdell, Henry H. Kim, and M. Ram Murty, Lectures on automorphic $L$-functions, Fields Institute Monographs, vol. 20, American Mathematical Society, Providence, RI, 2004. MR 2071722, DOI 10.1090/fim/020
Wee Teck Gan and Shuichiro Takeda, The local Langlands conjecture for $\textrm {GSp}(4)$, Ann. of Math. (2) 173 (2011), no. 3, 1841–1882. MR 2800725, DOI 10.4007/annals.2011.173.3.12
Stephen Gelbart and Hervé Jacquet, A relation between automorphic representations of $\textrm {GL}(2)$ and $\textrm {GL}(3)$, Ann. Sci. École Norm. Sup. (4) 11 (1978), no. 4, 471–542. MR 533066
Stephen Gelbart, Ilya Piatetski-Shapiro, and Stephen Rallis, Explicit constructions of automorphic $L$-functions, Lecture Notes in Mathematics, vol. 1254, Springer-Verlag, Berlin, 1987. MR 892097, DOI 10.1007/BFb0078125
Stephen Gelbart and Freydoon Shahidi, Analytic properties of automorphic $L$-functions, Perspectives in Mathematics, vol. 6, Academic Press, Inc., Boston, MA, 1988. MR 951897
Stephen S. Gelbart, Automorphic forms on adèle groups, Annals of Mathematics Studies, No. 83, Princeton University Press, Princeton, N.J.; University of Tokyo Press, Tokyo, 1975. MR 0379375
I. M. Gel′fand, M. I. Graev, and I. I. Pyatetskii-Shapiro, Representation theory and automorphic functions, Generalized Functions, vol. 6, Academic Press, Inc., Boston, MA, 1990. Translated from the Russian by K. A. Hirsch; Reprint of the 1969 edition. MR 1071179
Roger Godement and Hervé Jacquet, Zeta functions of simple algebras, Lecture Notes in Mathematics, Vol. 260, Springer-Verlag, Berlin-New York, 1972. MR 0342495
Michael Harris, Nick Shepherd-Barron, and Richard Taylor, A family of Calabi-Yau varieties and potential automorphy, Ann. of Math. (2) 171 (2010), no. 2, 779–813. MR 2630056, DOI 10.4007/annals.2010.171.779
Michael Harris and Richard Taylor, The geometry and cohomology of some simple Shimura varieties, Annals of Mathematics Studies, vol. 151, Princeton University Press, Princeton, NJ, 2001. With an appendix by Vladimir G. Berkovich. MR 1876802
Guy Henniart, Une preuve simple des conjectures de Langlands pour $\textrm {GL}(n)$ sur un corps $p$-adique, Invent. Math. 139 (2000), no. 2, 439–455 (French, with English summary). MR 1738446, DOI 10.1007/s002220050012
H. Jacquet and R. P. Langlands, Automorphic forms on $\textrm {GL}(2)$, Lecture Notes in Mathematics, Vol. 114, Springer-Verlag, Berlin-New York, 1970. MR 0401654
Lizhen Ji, Kefeng Liu, Shing-Tung Yau, and Zhu-Jun Zheng (eds.), Automorphic forms and the Langlands program, Advanced Lectures in Mathematics (ALM), vol. 9, International Press, Somerville, MA; Higher Education Press, Beijing, 2010. Including papers from the International Conference “Langlands and Geometric Langlands Program” held in Guangzhou, June 18–21, 2007. MR 2640472
Henry H. Kim, Functoriality for the exterior square of $\textrm {GL}_4$ and the symmetric fourth of $\textrm {GL}_2$, J. Amer. Math. Soc. 16 (2003), no. 1, 139–183. With appendix 1 by Dinakar Ramakrishnan and appendix 2 by Kim and Peter Sarnak. MR 1937203, DOI 10.1090/S0894-0347-02-00410-1
Henry H. Kim and Freydoon Shahidi, Functorial products for $\textrm {GL}_2\times \textrm {GL}_3$ and the symmetric cube for $\textrm {GL}_2$, Ann. of Math. (2) 155 (2002), no. 3, 837–893. With an appendix by Colin J. Bushnell and Guy Henniart. MR 1923967, DOI 10.2307/3062134
Laurent Lafforgue, Chtoucas de Drinfeld et correspondance de Langlands, Invent. Math. 147 (2002), no. 1, 1–241 (French, with English and French summaries). MR 1875184, DOI 10.1007/s002220100174
R. P. Langlands, Problems in the theory of automorphic forms, Lectures in modern analysis and applications, III, Lecture Notes in Math., Vol. 170, Springer, Berlin, 1970, pp. 18–61. MR 0302614
Robert P. Langlands, Euler products, Yale Mathematical Monographs, vol. 1, Yale University Press, New Haven, Conn.-London, 1971. A James K. Whittemore Lecture in Mathematics given at Yale University, 1967. MR 0419366
Robert P. Langlands, On the functional equations satisfied by Eisenstein series, Lecture Notes in Mathematics, Vol. 544, Springer-Verlag, Berlin-New York, 1976. MR 0579181
Robert P. Langlands, Base change for $\textrm {GL}(2)$, Annals of Mathematics Studies, No. 96, Princeton University Press, Princeton, N.J.; University of Tokyo Press, Tokyo, 1980. MR 574808
C. Mœglin and J.-L. Waldspurger, Spectral decomposition and Eisenstein series, Cambridge Tracts in Mathematics, vol. 113, Cambridge University Press, Cambridge, 1995. Une paraphrase de l’Écriture [A paraphrase of Scripture]. MR 1361168, DOI 10.1017/CBO9780511470905
Bao Châu Ngô, Le lemme fondamental pour les algèbres de Lie, Publ. Math. Inst. Hautes Études Sci. 111 (2010), 1–169 (French). MR 2653248, DOI 10.1007/s10240-010-0026-7
Stephen Rallis, Langlands’ functoriality and the Weil representation, Amer. J. Math. 104 (1982), no. 3, 469–515. MR 658543, DOI 10.2307/2374151
Dinakar Ramakrishnan, Modularity of the Rankin-Selberg $L$-series, and multiplicity one for $\textrm {SL}(2)$, Ann. of Math. (2) 152 (2000), no. 1, 45–111. MR 1792292, DOI 10.2307/2661379
Jonathan D. Rogawski, Automorphic representations of unitary groups in three variables, Annals of Mathematics Studies, vol. 123, Princeton University Press, Princeton, NJ, 1990. MR 1081540, DOI 10.1515/9781400882441
Andrew Wiles, Modular elliptic curves and Fermat’s last theorem, Ann. of Math. (2) 141 (1995), no. 3, 443–551. MR 1333035, DOI 10.2307/2118559
Peter Sarnak and Freydoon Shahidi (eds.), Automorphic forms and applications, IAS/Park City Mathematics Series, vol. 12, American Mathematical Society, Providence, RI; Institute for Advanced Study (IAS), Princeton, NJ, 2007. Lecture notes from the IAS/Park City Mathematics Institute held in Park City, UT, July 1–20, 2002. MR 2331351, DOI 10.1090/pcms/012
Freydoon Shahidi, Eisenstein series and automorphic $L$-functions, American Mathematical Society Colloquium Publications, vol. 58, American Mathematical Society, Providence, RI, 2010. MR 2683009, DOI 10.1090/coll/058
J. T. Tate, Fourier analysis in number fields, and Hecke’s zeta-functions, Algebraic Number Theory (Proc. Instructional Conf., Brighton, 1965), Thompson, Washington, D.C., 1967, pp. 305–347. MR 0217026
Richard Taylor, Automorphy for some $l$-adic lifts of automorphic mod $l$ Galois representations. II, Publ. Math. Inst. Hautes Études Sci. 108 (2008), 183–239. MR 2470688, DOI 10.1007/s10240-008-0015-2
Richard Taylor and Andrew Wiles, Ring-theoretic properties of certain Hecke algebras, Ann. of Math. (2) 141 (1995), no. 3, 553–572. MR 1333036, DOI 10.2307/2118560
Andrew Wiles, Modular elliptic curves and Fermat’s last theorem, Ann. of Math. (2) 141 (1995), no. 3, 443–551. MR 1333035, DOI 10.2307/2118559
References
- James Arthur, The work of Ngô Bao Châu, Proceedings of the International Congress of Mathematicians. Volume I, Hindustan Book Agency, New Delhi, 2010, pp. 57–70. MR 2827882
- James Arthur and Laurent Clozel, Simple algebras, base change, and the advanced theory of the trace formula, Annals of Mathematics Studies, vol. 120, Princeton University Press, Princeton, NJ, 1989. MR 1007299 (90m:22041)
- Emil Artin and John Tate, Class field theory, AMS Chelsea Publishing, Providence, RI, 2009. Reprinted with corrections from the 1967 original. MR 2467155 (2009k:11001)
- Mahdi Asgari and Freydoon Shahidi, Generic transfer for general spin groups, Duke Math. J. 132 (2006), no. 1, 137–190. MR 2219256 (2007d:11055a), DOI 10.1215/S0012-7094-06-13214-3
- Mahdi Asgari and Freydoon Shahidi, Generic transfer from $\rm GSp(4)$ to $\rm GL(4)$, Compos. Math. 142 (2006), no. 3, 541–550. MR 2231191 (2007d:11055b), DOI 10.1112/S0010437X06001904
- A. Borel, Automorphic $L$-functions, Automorphic forms, representations and $L$-functions (Proc. Sympos. Pure Math., Oregon State Univ., Corvallis, Ore., 1977), Part 2, Proc. Sympos. Pure Math., XXXIII, Amer. Math. Soc., Providence, R.I., 1979, pp. 27–61. MR 546608 (81m:10056)
- Armand Borel and W. Casselman (eds.), Automorphic forms, representations and $L$-functions. Part 1, Proceedings of Symposia in Pure Mathematics, XXXIII, Providence, R.I., American Mathematical Society, 1979. MR 546586 (80g:10002a)
- Armand Borel and W. Casselman (eds.), Automorphic forms, representations, and $L$-functions. Part 2, Proceedings of Symposia in Pure Mathematics, XXXIII, Providence, R.I., American Mathematical Society, 1979. MR 546606 (80g:10002b)
- Armand Borel and George D. Mostow (eds.), Proceedings of Symposia in Pure Mathematics. Vol. IX: Algebraic groups and discontinuous subgroups, Proceedings of the Symposium in Pure Mathematics of the American Mathematical Society held at the University of Colorado, Boulder, Colorado (July 5-August 6, vol. 1965, American Mathematical Society, Providence, R.I., 1966. MR 0202512 (34:2381)
- Christophe Breuil, Brian Conrad, Fred Diamond, and Richard Taylor, On the modularity of elliptic curves over $\mathbf {Q}$: wild 3-adic exercises, J. Amer. Math. Soc. 14 (2001), no. 4, 843–939 (electronic). MR 1839918 (2002d:11058), DOI 10.1090/S0894-0347-01-00370-8
- D. Bump, J. W. Cogdell, E. de Shalit, D. Gaitsgory, E. Kowalski, and S. S. Kudla, An introduction to the Langlands program, Birkhäuser Boston Inc., Boston, MA, 2003. Lectures presented at the Hebrew University of Jerusalem, Jerusalem, March 12–16, 2001; Edited by Joseph Bernstein and Stephen Gelbart. MR 1990371 (2004g:11037)
- Daniel Bump, The Rankin-Selberg method: a survey, Number theory, trace formulas and discrete groups (Oslo, 1987) Academic Press, Boston, MA, 1989, pp. 49–109. MR 993311 (90m:11079)
- Daniel Bump, Automorphic forms and representations, Cambridge Studies in Advanced Mathematics, vol. 55, Cambridge University Press, Cambridge, 1997. MR 1431508 (97k:11080), DOI 10.1017/CBO9780511609572
- Daniel Bump, The Rankin-Selberg method: an introduction and survey, Automorphic representations, $L$-functions and applications: progress and prospects, Ohio State Univ. Math. Res. Inst. Publ., vol. 11, de Gruyter, Berlin, 2005, pp. 41–73. MR 2192819 (2006k:11097)
- William Casselman, Introduction to the representation theory of $p$-adic groups, http://www. math.ubc.ca/~cass/research/pdf/p-adic-book.pdf.
- Laurent Clozel, Michael Harris, and Richard Taylor, Automorphy for some $l$-adic lifts of automorphic mod $l$ Galois representations, Publ. Math. Inst. Hautes Études Sci. (2008), no. 108, 1–181, With Appendix A, summarizing unpublished work of Russ Mann, and Appendix B by Marie-France Vignéras. MR 2470687 (2010j:11082)
- J. W. Cogdell, Dual groups and Langlands functoriality, An introduction to the Langlands program (Jerusalem, 2001) Birkhäuser Boston, Boston, MA, 2003, pp. 251–268. MR 1990382
- J. W. Cogdell, H. H. Kim, I. I. Piatetski-Shapiro, and F. Shahidi, On lifting from classical groups to $\textrm {GL}_N$, Publ. Math. Inst. Hautes Études Sci. 93 (2001), 5–30. MR 1863734 (2002i:11048), DOI 10.1007/s10240-001-8187-z
- J. W. Cogdell, H. H. Kim, I. I. Piatetski-Shapiro, and F. Shahidi, Functoriality for the classical groups, Publ. Math. Inst. Hautes Études Sci. 99 (2004), 163–233. MR 2075885 (2006a:22010), DOI 10.1007/s10240-004-0020-z
- J. W. Cogdell and I. I. Piatetski-Shapiro, Converse theorems for $\textrm {GL}_n$, Inst. Hautes Études Sci. Publ. Math. 79 (1994), 157–214. MR 1307299 (95m:22009)
- J. W. Cogdell and I. I. Piatetski-Shapiro, Converse theorems for $\textrm {GL}_n$. II, J. Reine Angew. Math. 507 (1999), 165–188. MR 1670207 (2000a:22029), DOI 10.1515/crll.1999.507.165
- James W. Cogdell, $L$-functions and converse theorems for $\textrm {GL}_n$, Automorphic forms and applications, IAS/Park City Math. Ser., vol. 12, Amer. Math. Soc., Providence, RI, 2007, pp. 97–177. MR 2331345 (2008e:11060)
- James W. Cogdell, Henry H. Kim, and M. Ram Murty, Lectures on automorphic $L$-functions, Fields Institute Monographs, vol. 20, American Mathematical Society, Providence, RI, 2004. MR 2071722 (2005h:11104)
- Wee Teck Gan and Shuichiro Takeda, The local Langlands conjecture for $\textrm {GSp}(4)$, Ann. of Math. (2) 173 (2011), no. 3, 1841–1882. MR 2800725 (2012c:22019), DOI 10.4007/annals.2011.173.3.12
- Stephen Gelbart and Hervé Jacquet, A relation between automorphic representations of $\textrm {GL}(2)$ and $\textrm {GL}(3)$, Ann. Sci. École Norm. Sup. (4) 11 (1978), no. 4, 471–542. MR 533066 (81e:10025)
- Stephen Gelbart, Ilya Piatetski-Shapiro, and Stephen Rallis, Explicit constructions of automorphic $L$-functions, Lecture Notes in Mathematics, vol. 1254, Springer-Verlag, Berlin, 1987. MR 892097 (89k:11038)
- Stephen Gelbart and Freydoon Shahidi, Analytic properties of automorphic $L$-functions, Perspectives in Mathematics, vol. 6, Academic Press Inc., Boston, MA, 1988. MR 951897 (89f:11077)
- Stephen S. Gelbart, Automorphic forms on adèle groups, Princeton University Press, Princeton, N.J., 1975. Annals of Mathematics Studies, No. 83. MR 0379375 (52 \#280)
- I. M. Gel′fand, M. I. Graev, and I. I. Pyatetskii-Shapiro, Representation theory and automorphic functions, Generalized Functions, vol. 6, Academic Press Inc., Boston, MA, 1990. Translated from the Russian by K. A. Hirsch; Reprint of the 1969 edition. MR 1071179 (91g:11052)
- Roger Godement and Hervé Jacquet, Zeta functions of simple algebras, Lecture Notes in Mathematics, Vol. 260, Springer-Verlag, Berlin, 1972. MR 0342495 (49 \#7241)
- Michael Harris, Nick Shepherd-Barron, and Richard Taylor, A family of Calabi-Yau varieties and potential automorphy, Ann. of Math. (2) 171 (2010), no. 2, 779–813. MR 2630056 (2011g:11106), DOI 10.4007/annals.2010.171.779
- Michael Harris and Richard Taylor, The geometry and cohomology of some simple Shimura varieties, Annals of Mathematics Studies, vol. 151, Princeton University Press, Princeton, NJ, 2001. With an appendix by Vladimir G. Berkovich. MR 1876802 (2002m:11050)
- Guy Henniart, Une preuve simple des conjectures de Langlands pour $\textrm {GL}(n)$ sur un corps $p$-adique, Invent. Math. 139 (2000), no. 2, 439–455 (French, with English summary). MR 1738446 (2001e:11052), DOI 10.1007/s002220050012
- H. Jacquet and R. P. Langlands, Automorphic forms on $\textrm {GL}(2)$, Lecture Notes in Mathematics, Vol. 114, Springer-Verlag, Berlin, 1970. MR 0401654 (53 \#5481)
- Lizhen Ji, Kefeng Liu, Shing-Tung Yau, and Zhu-Jun Zheng (eds.), Automorphic forms and the Langlands program, Advanced Lectures in Mathematics (ALM), vol. 9, International Press, Somerville, MA, 2010, Including papers from the International Conference “Langlands and Geometric Langlands Program” held in Guangzhou, June 18–21, 2007. MR 2640472 (2011i:22003)
- Henry H. Kim, Functoriality for the exterior square of $\textrm {GL}_4$ and the symmetric fourth of $\textrm {GL}_2$, J. Amer. Math. Soc. 16 (2003), no. 1, 139–183 (electronic). With appendix 1 by Dinakar Ramakrishnan and appendix 2 by Kim and Peter Sarnak. MR 1937203 (2003k:11083), DOI 10.1090/S0894-0347-02-00410-1
- Henry H. Kim and Freydoon Shahidi, Functorial products for $\textrm {GL}_2\times \textrm {GL}_3$ and the symmetric cube for $\textrm {GL}_2$, Ann. of Math. (2) 155 (2002), no. 3, 837–893. With an appendix by Colin J. Bushnell and Guy Henniart. MR 1923967 (2003m:11075), DOI 10.2307/3062134
- Laurent Lafforgue, Chtoucas de Drinfeld et correspondance de Langlands, Invent. Math. 147 (2002), no. 1, 1–241 (French, with English and French summaries). MR 1875184 (2002m:11039), DOI 10.1007/s002220100174
- R. P. Langlands, Problems in the theory of automorphic forms, Lectures in modern analysis and applications, III, Springer, Berlin, 1970, pp. 18–61. Lecture Notes in Math., Vol. 170. MR 0302614 (46 \#1758)
- Robert P. Langlands, Euler products, Yale University Press, New Haven, Conn., 1971. A James K. Whittemore Lecture in Mathematics given at Yale University, 1967; Yale Mathematical Monographs, 1. MR 0419366 (54 \#7387)
- Robert P. Langlands, On the functional equations satisfied by Eisenstein series, Lecture Notes in Mathematics, Vol. 544, Springer-Verlag, Berlin, 1976. MR 0579181 (58:28319)
- Robert P. Langlands, Base change for $\textrm {GL}(2)$, Annals of Mathematics Studies, vol. 96, Princeton University Press, Princeton, N.J., 1980. MR 574808 (82a:10032)
- C. Mœglin and J.-L. Waldspurger, Spectral decomposition and Eisenstein series, Cambridge Tracts in Mathematics, vol. 113, Cambridge University Press, Cambridge, 1995, Une paraphrase de l’Écriture [A paraphrase of Scripture]. MR 1361168 (97d:11083)
- Bao Châu Ngô, Le lemme fondamental pour les algèbres de Lie, Publ. Math. Inst. Hautes Études Sci. 111 (2010), 1–169 (French). MR 2653248 (2011h:22011), DOI 10.1007/s10240-010-0026-7
- Stephen Rallis, Langlands’ functoriality and the Weil representation, Amer. J. Math. 104 (1982), no. 3, 469–515. MR 658543 (84c:10025), DOI 10.2307/2374151
- Dinakar Ramakrishnan, Modularity of the Rankin-Selberg $L$-series, and multiplicity one for $\textrm {SL}(2)$, Ann. of Math. (2) 152 (2000), no. 1, 45–111. MR 1792292 (2001g:11077), DOI 10.2307/2661379
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- Yiannis Sakellaridis, Spherical varieties and integral representations of L-functions., Algebra and Number Theory 6 (2012), no. 4, 611–667. MR 1333035 (96d:11071)
- Peter Sarnak and Freydoon Shahidi (eds.), Automorphic forms and applications, IAS/Park City Mathematics Series, vol. 12, American Mathematical Society, Providence, RI, 2007, Lecture notes from the IAS/Park City Mathematics Institute held in Park City, UT, July 1–20, 2002. MR 2331351 (2008b:00004)
- Freydoon Shahidi, Eisenstein series and automorphic $L$-functions, American Mathematical Society Colloquium Publications, vol. 58, American Mathematical Society, Providence, RI, 2010. MR 2683009 (2012d:11119)
- J. T. Tate, Fourier analysis in number fields, and Hecke’s zeta-functions, Algebraic Number Theory (Proc. Instructional Conf., Brighton, 1965), Thompson, Washington, D.C., 1967, pp. 305–347. MR 0217026 (36 \#121)
- Richard Taylor, Automorphy for some $l$-adic lifts of automorphic mod $l$ Galois representations. II, Publ. Math. Inst. Hautes Études Sci. 108 (2008), 183–239. MR 2470688 (2010j:11085), DOI 10.1007/s10240-008-0015-2
- Richard Taylor and Andrew Wiles, Ring-theoretic properties of certain Hecke algebras, Ann. of Math. (2) 141 (1995), no. 3, 553–572. MR 1333036 (96d:11072), DOI 10.2307/2118560
- Andrew Wiles, Modular elliptic curves and Fermat’s last theorem, Ann. of Math. (2) 141 (1995), no. 3, 443–551. MR 1333035 (96d:11071), DOI 10.2307/2118559
Review Information:
Reviewer:
Ramin Takloo-Bighash
Affiliation:
University of Illinois at Chicago
Email:
rtakloo@math.uic.edu
Journal:
Bull. Amer. Math. Soc.
50 (2013), 645-654
DOI:
https://doi.org/10.1090/S0273-0979-2013-01399-5
Published electronically:
January 17, 2013
Additional Notes:
While writing this article the author was partially supported by a grant from the National Security Agency (Award number 111011) and a grant from the Simons Foundation (Award number 245977). I wish to thank Dorian Goldfeld, Joseph Hundley, Peter Kuchment, Kimball Martin, Dipendra Prasad, and Yiannis Sakellaridis for useful communications.
Review copyright:
© Copyright 2013
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.
