American Mathematical Society

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

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
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
Richard E. Borcherds, Automorphic forms on ${\rm O}_{s+2,2}({\bf R})$ and infinite products, Invent. Math. 120 (1995), no. 1, 161–213. MR 1323986, DOI https://doi.org/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 https://doi.org/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 https://doi.org/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 https://doi.org/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
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 https://doi.org/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 https://doi.org/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 https://doi.org/10.2206/kyushumfs.46.307
Jean-Pierre Serre, Valeurs propres des opérateurs de Hecke modulo $l$, Journées Arithmétiques de Bordeaux (Conf., Univ. Bordeaux, 1974), Soc. Math. France, Paris, 1975, pp. 109–117. Astérisque, Nos. 24-25 (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 https://doi.org/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, 1972) Springer, Berlin, 1973, pp. 1–55. Lecture Notes in Math., Vol. 350. 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