Bulletin of the American Mathematical Society

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Book Information:

Author: Carlos Moreno
Title: Advanced analytic number theory: L-functions
Additional book information: Mathematical Surveys and Monographs, vol. 115, American Mathematical Society, Providence, RI, 2005, xx+291 pp., ISBN 978-0-8218-3641-5, US$76.00$

James Arthur, Harmonic analysis and group representations, Notices Amer. Math. Soc. 47 (2000), no. 1, 26–34. MR 1733064

Farrell Brumley, Effective multiplicity one on $\textrm {GL}_N$ and narrow zero-free regions for Rankin-Selberg $L$-functions, Amer. J. Math. 128 (2006), no. 6, 1455–1474. MR 2275908

Daniel Bump, Solomon Friedberg, and Jeffrey Hoffstein, On some applications of automorphic forms to number theory, Bull. Amer. Math. Soc. (N.S.) 33 (1996), no. 2, 157–175. MR 1359575, DOI 10.1090/S0273-0979-96-00654-4

Stephen S. Gelbart, Erez M. Lapid, and Peter Sarnak, A new method for lower bounds of $L$-functions, C. R. Math. Acad. Sci. Paris 339 (2004), no. 2, 91–94 (English, with English and French summaries). MR 2078295, DOI 10.1016/j.crma.2004.04.024

Stephen Gelbart and Freydoon Shahidi, Boundedness of automorphic $L$-functions in vertical strips, J. Amer. Math. Soc. 14 (2001), no. 1, 79–107. MR 1800349, DOI 10.1090/S0894-0347-00-00351-9

[Har]

M. Harris, ``Review of Introduction to the Langlands Program'', Bull. Amer. Math. Soc. (N.S.), 41 (2004), 257-266.

Henryk Iwaniec and Emmanuel Kowalski, Analytic number theory, American Mathematical Society Colloquium Publications, vol. 53, American Mathematical Society, Providence, RI, 2004. MR 2061214, DOI 10.1090/coll/053

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, DOI 10.2307/2374103

[Kow]

E. Kowalski, ``Elementary Theory of L-functions'', An Introduction to the Langlands Program, Birkhäuser, Boston, 2003.

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

Jianya Liu, Yonghui Wang, and Yangbo Ye, A proof of Selberg’s orthogonality for automorphic $L$-functions, Manuscripta Math. 118 (2005), no. 2, 135–149. MR 2177681, DOI 10.1007/s00229-005-0563-4

[Mic]

P. Michel, Analytic Number Theory and Families of Automorphic L-Functions, to appear.

C. J. Moreno, Explicit formulas in the theory of automorphic forms, Number Theory day (Proc. Conf., Rockefeller Univ., New York, 1976) Lecture Notes in Math., Vol. 626, Springer, Berlin, 1977, pp. 73–216. MR 0476650

Carlos J. Moreno, Analytic proof of the strong multiplicity one theorem, Amer. J. Math. 107 (1985), no. 1, 163–206. MR 778093, DOI 10.2307/2374461

M. Ram Murty and V. Kumar Murty, Non-vanishing of $L$-functions and applications, Progress in Mathematics, vol. 157, Birkhäuser Verlag, Basel, 1997. MR 1482805, DOI 10.1007/978-3-0348-0274-1

Zeév Rudnick and Peter Sarnak, Zeros of principal $L$-functions and random matrix theory, Duke Math. J. 81 (1996), no. 2, 269–322. A celebration of John F. Nash, Jr. MR 1395406, DOI 10.1215/S0012-7094-96-08115-6

Peter Sarnak, Nonvanishing of $L$-functions on $\mathfrak {R}(s)=1$, Contributions to automorphic forms, geometry, and number theory, Johns Hopkins Univ. Press, Baltimore, MD, 2004, pp. 719–732. MR 2058625

Atle Selberg, Old and new conjectures and results about a class of Dirichlet series, Proceedings of the Amalfi Conference on Analytic Number Theory (Maiori, 1989) Univ. Salerno, Salerno, 1992, pp. 367–385. MR 1220477

Freydoon Shahidi, Automorphic $L$-functions and functoriality, Proceedings of the International Congress of Mathematicians, Vol. II (Beijing, 2002) Higher Ed. Press, Beijing, 2002, pp. 655–666. MR 1957073

[Art]

J. Arthur, ``Harmonic Analysis and Group Representations'', Notices of A.M.S., 47 (2000), no. 1, 26-34. MR 1733064

[Bru]

F. Brumley, ``Effective Multiplicity One for and Narrow Zero-free Regions for Rankin-Selberg -functions'', Amer. J. Math., 128 (2006), no. 6, 1455-1474. MR 2275908

[BFH]

D. Bump, S. Friedberg, and J. Hoffstein, ``On Some Applications of Automorphic Forms to Number Theory'', Bull. Amer. Math. Soc. (N.S.), 33 (1996), 157-175. MR 1359575 (97a:11072)

[GLS]

S. Gelbart, E. Lapid, and P. Sarnak, ``A New Method for Lower Bounds of L-functions'', C. R. Acad. Sci. Paris, Ser. I, 399 (2004), 91-94; also see S. Gelbart and E. Lapid, ``Lower Bounds for L-functions at the Edge of the Critical Strip'', Amer. J. Math., 128 (2006), 619-638. MR 2078295 (2005f:11197), MR 2230919 (2007d:11057)

[GeS]

S. Gelbart and F. Shahidi, ``Boundedness of Automorphic L-Functions in Vertical Strips'', J. Amer. Math. Soc., 41 (2001), 79-107. MR 1800349 (2003a:11056)

[Har]

M. Harris, ``Review of Introduction to the Langlands Program'', Bull. Amer. Math. Soc. (N.S.), 41 (2004), 257-266.

[IwK]

H. Iwaniec and E. Kowalski, Analytic Number Theory, American Math. Society Colloquium Publication, Vol. 53, 2004. MR 2061214 (2005h:11005)

[JSh]

H. Jacquet and J. Shalika, ``On Euler Products and the Classification of Automorphic Representations'', Amer. J. Math., 103 (1981), 499-558, 777-815. MR 0618323 (82m:10050a), MR 0623137(82m:10050b)

[Kow]

E. Kowalski, ``Elementary Theory of L-functions'', An Introduction to the Langlands Program, Birkhäuser, Boston, 2003.

[Lan]

R. Langlands, ``Problems in the Theory of Automorphic Forms'', Lectures in Modern Analysis and Applications, Lecture Notes in Math., vol. 170, Springer-Verlag, New York, 1970, pp. 18-86. MR 0302614 (46:1758)

[LWY]

J. Liu, Y. Wang, and Y. Ye, ``A Proof of Selberg's Orthogonality for Automorphic L-Functions'', Manuscripta Math., 118 (2005), 135-149. MR 2177681 (2006j:11072)

[Mic]

P. Michel, Analytic Number Theory and Families of Automorphic L-Functions, to appear.

[Mor1]

C. Moreno, ``Explicit Formulas in the Automorphic Forms'', Number Theory Day: Proceedings, New York, 1976, Lecture Notes in Math., vol. 627, Springer-Verlag, 1977, pp. 73-216. MR 0476650 (57:16209)

[Mor2]

C. Moreno, ``Analytic Proof of the Strong Multiplicity One Theorem'', Amer. J. Math., 107 (1985), 163-206. MR 778093 (86m:22027)

[Mur]

R. Murty and K. Murty, Non-vanishing of L-functions and Applications, Progress in Mathematics, vol. 157, Birkhäuser-Verlag, Basel-Boston-Berlin, 1997. MR 1482805 (98h:11106)

[RuS]

Z. Rudnick and P. Sarnak, ``Zeros of Principal L-functions and Random Matrix Theory'', Duke Math. J., 81 (1996), 269-322. MR 1395406 (97f:11074)

[Sar]

P. Sarnak, ``Non-vanishing of L-functions on Re(s)=1'', Contributions to Automorphic Forms, Geometry, and Number Theory, Johns Hopkins Univ. Press, Baltimore, 2004, pp. 719-732. MR 2058625 (2005f:11184)

[Sel]

A. Selberg, ``Old and New Conjectures and Results about a Class of Dirichlet Series'', Collected Papers, Vol. II, Springer-Verlag, pp. 47-63. MR 1220477 (94f:11085)

[Sha]

F. Shahidi, ``Automorphic L-functions and Functoriality'', International Cong. of Mathematicians, Vol. III (2002), pp. 655-666. MR 1957073 (2003k:11084)