Book Review
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MathSciNet review: 2507285
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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