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Book Information:

Author: A. Borel
Title: Automorphic forms on $SL_{2}(\mathbf{R})$
Additional book information: Cambridge Tracts in Mathematics, vol. 130, Cambridge University Press, 1997, xiv+574 pp., ISBN 0-521-58049-8, $47.95

Author: D. Bump
Title: Automorphic forms and representations
Additional book information: Cambridge Studies in Advanced Mathematics, vol. 55, Cambridge University Press, 1997, xiv+574 pp., ISBN 0-521-55098-X, $79.95

Author: H. Iwaniec
Title: Topics in classical automorphic forms
Additional book information: Graduate Studies in Math., vol. 17, American Mathematical Society, Providence, RI, 1997, xii + 259 pp., ISBN 0-8218-0777-3, $39.00

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  • [AR] J. Adams and B. Roberts, Notes on the theta correspondence, Workshop at U. Maryland, 1994, www.math.umd.edu/~jda/preprints.
  • [A1] J. Arthur, Stability and endoscopy: informal motivation, In: [BK]. CMP 98:03
  • [A2] James Arthur, Unipotent automorphic representations: conjectures, Astérisque 171-172 (1989), 13–71. Orbites unipotentes et représentations, II. MR 1021499
  • [A3] J. Arthur, The problem of classifying automorphic representations of classical groups, CRM Proceedings and Lecture Notes, vol. 11, Amer. Math. Soc., Providence, RI, 1997. CMP 98:04
  • [A4] James Arthur, The Selberg trace formula for groups of 𝐹-rank one, Ann. of Math. (2) 100 (1974), 326–385. MR 0360470
  • [AC] 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
  • [BR] Don Blasius and Jonathan D. Rogawski, Zeta functions of Shimura varieties, Motives (Seattle, WA, 1991) Proc. Sympos. Pure Math., vol. 55, Amer. Math. Soc., Providence, RI, 1994, pp. 525–571. MR 1265563
  • [Bo] A. Borel, Automorphic forms on SL$_{2}(\mathbf{R),}$ Cambridge Tracts in Math. 130, Cambridge U. Press, 1997. CMP 98:04
  • [BC] 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
  • [BM] 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
  • [BK] T. N. Bailey and A. W. Knapp (eds.), Representation theory and automorphic forms, Proc. Symposia in Pure Math. 61, AMS, Providence 1997. CMP 98:03
  • [Bu] Daniel Bump, Automorphic forms and representations, Cambridge Studies in Advanced Mathematics, vol. 55, Cambridge University Press, Cambridge, 1997. MR 1431508
  • [BuK] Colin J. Bushnell and Philip C. Kutzko, The admissible dual of 𝐺𝐿(𝑁) via compact open subgroups, Annals of Mathematics Studies, vol. 129, Princeton University Press, Princeton, NJ, 1993. MR 1204652
  • [CM] Laurent Clozel and James S. Milne (eds.), Automorphic forms, Shimura varieties, and 𝐿-functions. Vol. I, Perspectives in Mathematics, vol. 10, Academic Press, Inc., Boston, MA, 1990. MR 1044817
    Laurent Clozel and James S. Milne (eds.), Automorphic forms, Shimura varieties, and 𝐿-functions. Vol. II, Perspectives in Mathematics, vol. 11, Academic Press, Inc., Boston, MA, 1990. MR 1044825
  • [De] P. Deligne, Correction to: “Formes modulaires et représentations de 𝐺𝐿(2)” (Modular functions of one variable, II (Proc. Internat. Summer School, Univ. Antwerp, Antwerp, 1972), pp. 55–105, Lecture Notes in Math., Vol. 349, Springer, Berlin, 1973), Modular functions of one variable, IV (Proc. Internat. Summer School, Univ. Antwerp, Antwerp, 1972) Springer, Berlin, 1975, pp. p. 148. Lecture Notes in Math., Vol. 476 (French). MR 0389771
  • [DL] Michel Duflo and Jean-Pierre Labesse, Sur la formule des traces de Selberg, Ann. Sci. École Norm. Sup. (4) 4 (1971), 193–284. MR 0437462
  • [Du] William Duke, Some old problems and new results about quadratic forms, Notices Amer. Math. Soc. 44 (1997), no. 2, 190–196. MR 1426107
  • [G1] Stephen S. Gelbart, Automorphic forms on adèle groups, Princeton University Press, Princeton, N.J.; University of Tokyo Press, Tokyo, 1975. Annals of Mathematics Studies, No. 83. MR 0379375
  • [G2] Stephen Gelbart, An elementary introduction to the Langlands program, Bull. Amer. Math. Soc. (N.S.) 10 (1984), no. 2, 177–219. MR 733692, 10.1090/S0273-0979-1984-15237-6
  • [G3] Stephen Gelbart, Lectures on the Arthur-Selberg trace formula, University Lecture Series, vol. 9, American Mathematical Society, Providence, RI, 1996. MR 1410260
  • [GJ] Stephen Gelbart and Hervé Jacquet, Forms of 𝐺𝐿(2) from the analytic point of view, 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. 213–251. MR 546600
  • [GS] Stephen Gelbart and Freydoon Shahidi, Analytic properties of automorphic 𝐿-functions, Perspectives in Mathematics, vol. 6, Academic Press, Inc., Boston, MA, 1988. MR 951897
  • [GGPS] I. M. Gel′fand, M. I. Graev, and I. I. Pyatetskii-Shapiro, Representation theory and automorphic functions, Translated from the Russian by K. A. Hirsch, W. B. Saunders Co., Philadelphia, Pa.-London-Toronto, Ont., 1969. MR 0233772
  • [He] Dennis A. Hejhal, The Selberg trace formula for 𝑃𝑆𝐿(2,𝑅). Vol. I, Lecture Notes in Mathematics, Vol. 548, Springer-Verlag, Berlin-New York, 1976. MR 0439755
  • [Hi] Haruzo Hida, Elementary theory of 𝐿-functions and Eisenstein series, London Mathematical Society Student Texts, vol. 26, Cambridge University Press, Cambridge, 1993. MR 1216135
  • [Ho] R. Howe, 𝜃-series and invariant theory, 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. 275–285. MR 546602
  • [I1] Henryk Iwaniec, Topics in classical automorphic forms, Graduate Studies in Mathematics, vol. 17, American Mathematical Society, Providence, RI, 1997. MR 1474964
  • [I2] Henryk Iwaniec, Introduction to the spectral theory of automorphic forms, Biblioteca de la Revista Matemática Iberoamericana. [Library of the Revista Matemática Iberoamericana], Revista Matemática Iberoamericana, Madrid, 1995. MR 1325466
  • [I3] Henryk Iwaniec, Fourier coefficients of modular forms of half-integral weight, Invent. Math. 87 (1987), no. 2, 385–401. MR 870736, 10.1007/BF01389423
  • [J1] H. Jacquet, Note on the analytic continuation of Eisenstein series, In [BK], 443-455. CMP 98:03
  • [J2] H. Jacquet, Principal L-functions for $\mathrm{GL}(n)$, In [BK], 321-329. CMP 98:03
  • [JL] H. Jacquet and R. P. Langlands, Automorphic forms on 𝐺𝐿(2), Lecture Notes in Mathematics, Vol. 114, Springer-Verlag, Berlin-New York, 1970. MR 0401654
  • [JS] H. Jacquet and J. A. Shalika, On Euler products and the classification of automorphic representations. I, Amer. J. Math. 103 (1981), no. 3, 499–558. MR 618323, 10.2307/2374103
    H. Jacquet and J. A. Shalika, On Euler products and the classification of automorphic forms. II, Amer. J. Math. 103 (1981), no. 4, 777–815. MR 623137, 10.2307/2374050
  • [K1] A. Knapp, Introduction to the Langlands Program, In [BK], 245-302. CMP 98:03
  • [K2] A. Knapp, Theoretical aspects of the trace formula for GL(2), In [BK], 355-405. CMP 98:03
  • [Ko] Robert E. Kottwitz, Stable trace formula: elliptic singular terms, Math. Ann. 275 (1986), no. 3, 365–399. MR 858284, 10.1007/BF01458611
  • [Ku] Stephen S. Kudla, The local Langlands correspondence: the non-Archimedean case, Motives (Seattle, WA, 1991) Proc. Sympos. Pure Math., vol. 55, Amer. Math. Soc., Providence, RI, 1994, pp. 365–391. MR 1265559
  • [L1] 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
  • [L2] Robert P. Langlands, Base change for 𝐺𝐿(2), Annals of Mathematics Studies, vol. 96, Princeton University Press, Princeton, N.J.; University of Tokyo Press, Tokyo, 1980. MR 574808
  • [L3] R. Langlands, Where stands functoriality today?, In [BK], 457-471. CMP 98:03
  • [L4] Robert P. Langlands, Representation theory: its rise and its role in number theory, Proceedings of the Gibbs Symposium (New Haven, CT, 1989) Amer. Math. Soc., Providence, RI, 1990, pp. 181–210. MR 1095333
  • [LR] Robert P. Langlands and Dinakar Ramakrishnan (eds.), The zeta functions of Picard modular surfaces, Université de Montréal, Centre de Recherches Mathématiques, Montreal, QC, 1992. MR 1155223
  • [LS] R. P. Langlands and D. Shelstad, On the definition of transfer factors, Math. Ann. 278 (1987), no. 1-4, 219–271. MR 909227, 10.1007/BF01458070
  • [La] Gérard Laumon, Cohomology of Drinfeld modular varieties. Part I, Cambridge Studies in Advanced Mathematics, vol. 41, Cambridge University Press, Cambridge, 1996. Geometry, counting of points and local harmonic analysis. MR 1381898
    Gérard Laumon, Cohomology of Drinfeld modular varieties. Part II, Cambridge Studies in Advanced Mathematics, vol. 56, Cambridge University Press, Cambridge, 1997. Automorphic forms, trace formulas and Langlands correspondence; With an appendix by Jean-Loup Waldspurger. MR 1439250
  • [LRS] W. Luo, Z. Rudnick, and P. Sarnak, On Selberg’s eigenvalue conjecture, Geom. Funct. Anal. 5 (1995), no. 2, 387–401. MR 1334872, 10.1007/BF01895672
  • [MW] 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
  • [Mo] C. Moeglin, Representations of $\emph{GL(n,F)}$ in the non-archimedean case, In [BK], 303-319. CMP 98:03
  • [Pr] D. Prasad, A brief survey of the theta correspondence, Contemporary Math. 210, Amer. Math. Soc. (1998), 171-193. CMP 98:03
  • [Ra] Dinakar Ramakrishnan, Regulators, algebraic cycles, and values of 𝐿-functions, Algebraic 𝐾-theory and algebraic number theory (Honolulu, HI, 1987), Contemp. Math., vol. 83, Amer. Math. Soc., Providence, RI, 1989, pp. 183–310. MR 991982, 10.1090/conm/083/991982
  • [Ri] Kenneth A. Ribet, A modular construction of unramified 𝑝-extensions of𝑄(𝜇_{𝑝}), Invent. Math. 34 (1976), no. 3, 151–162. MR 0419403
  • [Ro] J. Rogawski, Functoriality and the Artin conjecture. In [BK], 331-353. CMP 98:03
  • [S1] Peter Sarnak, Some applications of modular forms, Cambridge Tracts in Mathematics, vol. 99, Cambridge University Press, Cambridge, 1990. MR 1102679
  • [S2] Peter Sarnak, On cusp forms, The Selberg trace formula and related topics (Brunswick, Maine, 1984), Contemp. Math., vol. 53, Amer. Math. Soc., Providence, RI, 1986, pp. 393–407. MR 853570, 10.1090/conm/053/853570
  • [S3] Peter Sarnak, Selberg’s eigenvalue conjecture, Notices Amer. Math. Soc. 42 (1995), no. 11, 1272–1277. MR 1355461
  • [Sel] Atle Selberg, Collected papers. Vol. I, Springer-Verlag, Berlin, 1989. With a foreword by K. Chandrasekharan. MR 1117906
  • [Ser] J.-P. Serre, A course in arithmetic, Springer-Verlag, New York-Heidelberg, 1973. Translated from the French; Graduate Texts in Mathematics, No. 7. MR 0344216
  • [Sh] Goro Shimura, Introduction to the arithmetic theory of automorphic functions, Publications of the Mathematical Society of Japan, vol. 11, Princeton University Press, Princeton, NJ, 1994. Reprint of the 1971 original; Kan\cflex o Memorial Lectures, 1. MR 1291394
  • [Wa] Jean-Loup Waldspurger, Représentation métaplectique et conjectures de Howe, Astérisque 152-153 (1987), 3, 85–99 (1988) (French). Séminaire Bourbaki, Vol. 1986/87. MR 936850
  • [W1] André Weil, Sur certains groupes d’opérateurs unitaires, Acta Math. 111 (1964), 143–211 (French). MR 0165033
  • [W2] André Weil, Elliptic functions according to Eisenstein and Kronecker, Springer-Verlag, Berlin-New York, 1976. Ergebnisse der Mathematik und ihrer Grenzgebiete, Band 88. MR 0562289

Review Information:

Reviewer: Jonathan D. Rogawski
Affiliation: University of California, Los Angeles
Email: jonr@math.ucla.edu
Journal: Bull. Amer. Math. Soc. 35 (1998), 253-263
DOI: http://dx.doi.org/10.1090/S0273-0979-98-00756-3
Review copyright: © Copyright 1998 American Mathematical Society