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ISSN 1088-9485(e) ISSN 0273-0979(p)

Book Review

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Book Information

Author(s): 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., (softcover) US $69.95, ISBN 978-3-540-74117-6

References:

1.: A. N. Andrianov, Quadratic forms and Hecke operators, Grund. der Math. 289, Springer-Verlag, Berlin (1987). MR 884891 (88g:11028)
2.: A. N. Andrianov and V. G. Zhuravlev, Modular forms and Hecke operators, translated from the Russian (1990) original by N. Koblitz. Translations of Mathematical Monographs 145, AMS, Providence, RI (1995). MR 1349824 (96d:11045)
3.: R. E. Borcherds, Automorphic forms on $O_{s+2,2}(\mathbb{R})$ and infinite products, Invent. Math. 120 (1995), 161-213. MR 1323986 (96j:11067)
4.: S. Breulmann and M. Kuss, On a conjecture of Duke-Omamoglu, Proc. AMS 128 (2000), 1595-1604. MR 1707138 (2000j:11065)
5.: J. H. Bruinier and T. Yang, CM values of Hilbert modular functions, Invent. Math. 163 (2006), 229-288. MR 2207018 (2008b:11053)
6.: P. Deligne and J. P. Serre, Formes modulaires de poids . Ann. Sci. École Norm. Sup. (4) 7 (1974), 507-530 (1975). MR 0379379 (52:284)
7.: W. Duke and O. Imamoglu, A converse theorem and the Saito-Kurokawa lift, Int. Math. Res. Not. 7 (1996), 347-355. MR 1389957 (97c:11052)
8.: E. Freitag, Siegelsche Modulfunktionen, Grund. der Math. Wiss. 254, Springer-Verlag, Berlin, (1983). MR 871067 (88b:11027)
9.: B. Gross and D. Zagier, On singular moduli, J. Reine Agnew. Math. 355 (1985), 191-220. MR 772491 (86j:11041)
10.: T. Ikeda, On the lifting of elliptic cusp forms to Siegel cusp forms of degree , Ann. of Math. 2 154 (2001), 641-681. MR 1884618 (2002m:11037)
11.: W. Kohnen, Lifting modular forms of half-integral weight to Siegel modular forms of even genus, Math. Ann 322 (2003), 787-809. MR 1905104 (2003d:11067)
12.: I. Miyawaki, Numerical examples of Siegel cusp forms of degree and their zeta-functions, Mem. Fac. Sci. Kyushu Univ. Ser. A 46 (1992), no. 2, 307-339. MR 1195472 (94e:11049)
13.: J. P. Serre, Valeurs propres des opérateurs de Hecke modulo , Journés Arithmétiques de Bordeaux (Conf., Univ. Bordeaux, 1974), 109-117. Asterisque, Nos. 24-25, Soc. Math. France, Paris, 1975. MR 0382173 (52:3061)
14.: G. Shimura, On modular correspondences for $\textnormal{Sp}_n(\mathbb{Z})$ and their congruence relations, Proc. Ac. Sci. USA 49 (1963), 824-828. MR 0157009 (28:250)
15.: P. Swinnerton-Dyer, On $\ell$ -adic representations and congruences for coefficients of modular forms, Modular functions of one variable, III (Proc. Internat. Summer School, Univ. Antwerp, 1972), 1-55. Lecture Notes in Math., Vol. 350, Springer, Berlin, 1973. MR 0406931 (53:10717a)

Additional Information:

Reviewer(s):
Amanda Folsom
Affiliation: University of Wisconsin, Madison
Email: folsom@math.wisc.edu

Review Information:
Journal: Bull. Amer. Math. Soc. 46 (2009), 527-533.

MSC (2000): Primary 11F11, 11F41, 11F46
DOI: 10.1090/S0273-0979-09-01256-7
PII: S 0273-0979(09)01256-7
Posted: March 23, 2009
Copyright of article: Copyright 2009, American Mathematical Society

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