Skip to Main Content

Bulletin of the American Mathematical Society

The Bulletin publishes expository articles on contemporary mathematical research, written in a way that gives insight to mathematicians who may not be experts in the particular topic. The Bulletin also publishes reviews of selected books in mathematics and short articles in the Mathematical Perspectives section, both by invitation only.

ISSN 1088-9485 (online) ISSN 0273-0979 (print)

The 2020 MCQ for Bulletin of the American Mathematical Society is 0.84.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

 

Book Review

The AMS does not provide abstracts of book reviews. You may download the entire review from the links below.


MathSciNet review: 2507285
Full text of review: PDF   This review is available free of charge.
Book Information:

Authors: J. H. Bruinier, G. van der Geer, G. Harder and D. Zagier
Title: The 1-2-3 of modular forms
Additional book information: Universitext, Springer-Verlag, Berlin, Heidelberg, 2008, x+266 pp., ISBN 978-3-540-74117-6, US $69.95$, softcover

References [Enhancements On Off] (What's this?)

  • Anatolij N. Andrianov, Quadratic forms and Hecke operators, Grundlehren der mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 286, Springer-Verlag, Berlin, 1987. MR 884891, DOI 10.1007/978-3-642-70341-6
  • A. N. Andrianov and V. G. Zhuravlëv, Modular forms and Hecke operators, Translations of Mathematical Monographs, vol. 145, American Mathematical Society, Providence, RI, 1995. Translated from the 1990 Russian original by Neal Koblitz. MR 1349824, DOI 10.1090/mmono/145
  • Richard E. Borcherds, Automorphic forms on $\textrm {O}_{s+2,2}(\textbf {R})$ and infinite products, Invent. Math. 120 (1995), no. 1, 161–213. MR 1323986, DOI 10.1007/BF01241126
  • Stefan Breulmann and Michael Kuss, On a conjecture of Duke-Imamoḡlu, Proc. Amer. Math. Soc. 128 (2000), no. 6, 1595–1604. MR 1707138, DOI 10.1090/S0002-9939-00-05586-6
  • Jan Hendrik Bruinier and Tonghai Yang, CM-values of Hilbert modular functions, Invent. Math. 163 (2006), no. 2, 229–288. MR 2207018, DOI 10.1007/s00222-005-0459-7
  • Pierre Deligne and Jean-Pierre Serre, Formes modulaires de poids $1$, Ann. Sci. École Norm. Sup. (4) 7 (1974), 507–530 (1975) (French). MR 379379
  • W. Duke and Ö. Imamoḡlu, A converse theorem and the Saito-Kurokawa lift, Internat. Math. Res. Notices 7 (1996), 347–355. MR 1389957, DOI 10.1155/S1073792896000220
  • E. Freitag, Siegelsche Modulfunktionen, Grundlehren der mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 254, Springer-Verlag, Berlin, 1983 (German). MR 871067, DOI 10.1007/978-3-642-68649-8
  • Benedict H. Gross and Don B. Zagier, On singular moduli, J. Reine Angew. Math. 355 (1985), 191–220. MR 772491
  • Tamotsu Ikeda, On the lifting of elliptic cusp forms to Siegel cusp forms of degree $2n$, Ann. of Math. (2) 154 (2001), no. 3, 641–681. MR 1884618, DOI 10.2307/3062143
  • Winfried Kohnen, Lifting modular forms of half-integral weight to Siegel modular forms of even genus, Math. Ann. 322 (2002), no. 4, 787–809. MR 1905104, DOI 10.1007/s002080100285
  • Isao Miyawaki, Numerical examples of Siegel cusp forms of degree $3$ and their zeta-functions, Mem. Fac. Sci. Kyushu Univ. Ser. A 46 (1992), no. 2, 307–339. MR 1195472, DOI 10.2206/kyushumfs.46.307
  • Jean-Pierre Serre, Valeurs propres des opérateurs de Hecke modulo $l$, Journées Arithmétiques de Bordeaux (Conf., Univ. Bordeaux, 1974), Astérisque, Nos. 24-25, Soc. Math. France, Paris, 1975, pp. 109–117 (French). MR 0382173
  • Goro Shimura, On modular correspondences for $Sp(n,\,Z)$ and their congruence relations, Proc. Nat. Acad. Sci. U.S.A. 49 (1963), 824–828. MR 157009, DOI 10.1073/pnas.49.6.824
  • H. P. F. Swinnerton-Dyer, On $l$-adic representations and congruences for coefficients of modular forms, Modular functions of one variable, III (Proc. Internat. Summer School, Univ. Antwerp, Antwerp, 1972) Lecture Notes in Math., Vol. 350, Springer, Berlin, 1973, pp. 1–55. MR 0406931

  • Review Information:

    Reviewer: Amanda Folsom
    Affiliation: University of Wisconsin, Madison
    Email: folsom@math.wisc.edu
    Journal: Bull. Amer. Math. Soc. 46 (2009), 527-533
    DOI: https://doi.org/10.1090/S0273-0979-09-01256-7
    Published electronically: March 23, 2009
    Review copyright: © Copyright 2009 American Mathematical Society