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Book Review
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Book Information
Author(s):
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.,
US$76.00,
ISBN 978-0-8218-3641-5
References:
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- [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)
Additional Information:
Reviewer(s):
S.
Gelbart
Affiliation:
Weizmann Institute of Science
Email:
stephen.gelbart@weizmann.ac.il
Review Information:
Journal:
Bull. Amer. Math. Soc.
45
(2008),
169-175.
MSC
(2000):
Primary 11Mxx, 11Rxx, 22Exx;
Secondary 11Sxx
PII:
S 0273-0979(07)01158-5
Posted:
June 8, 2007
Copyright of article:
Copyright
2007,
American Mathematical Society
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