Book Review

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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$76.00$

*Harmonic analysis and group representations*, Notices Amer. Math. Soc.

**47**(2000), no. 1, 26–34. MR

**1733064**

*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**

*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

*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

*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]**

*Introduction to the Langlands Program*'',

*Bull. Amer. Math. Soc. (N.S.)*, 41 (2004), 257-266.

*Analytic number theory*, American Mathematical Society Colloquium Publications, vol. 53, American Mathematical Society, Providence, RI, 2004. MR

**2061214**, DOI 10.1090/coll/053

*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]**

*An Introduction to the Langlands Program*, Birkhäuser, Boston, 2003.

*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**

*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]**

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

*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**

*Analytic proof of the strong multiplicity one theorem*, Amer. J. Math.

**107**(1985), no. 1, 163–206. MR

**778093**, DOI 10.2307/2374461

*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

*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

*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**

*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**

*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**

Review Information:

Reviewer: S. Gelbart

Affiliation: Weizmann Institute of Science

Email: stephen.gelbart@weizmann.ac.il

Journal: Bull. Amer. Math. Soc.

**45**(2008), 169-175

Published electronically: June 8, 2007

Review copyright: © Copyright 2007 American Mathematical Society