Modular Forms on Schiermonnikoog

A collection of articles presenting the state of the art in the topic of modular forms.

Bas Edixhoven (Edited by), Gerard van der Geer (Edited by), Ben Moonen (Edited by)

9780521493543, Cambridge University Press

Hardback, published 27 November 2008

360 pages, 20 tables
23.4 x 15.7 x 2.3 cm, 0.62 kg

Modular forms are functions with an enormous amount of symmetry that play a central role in number theory, connecting it with analysis and geometry. They have played a prominent role in mathematics since the 19th century and their study continues to flourish today. Modular forms formed the inspiration for Langlands' conjectures and play an important role in the description of the cohomology of varieties defined over number fields. This collection of up-to-date articles originated from the conference 'Modular Forms' held on the Island of Schiermonnikoog in the Netherlands. A broad range of topics is covered including Hilbert and Siegel modular forms, Weil representations, Tannakian categories and Torelli's theorem. This book is a good source for all researchers and graduate students working on modular forms or related areas of number theory and algebraic geometry.

Preface
Contributors
1. Modular forms Bas Edixhoven, Gerard van der Geer and Ben Moonen
2. On the basis problem for Siegel modular forms with level Siegfried Böcherer, Hidenori Katsurada and Rainer Shulze-Pillot
3. Mock theta functions, weak Maass forms, and applications Kathrin Bringmann
4. Sign changes of coefficients of half integral weight modular forms Jan Hendrik Bruinier and Winfried Kohnen
5. Gauss map on the theta divisor and Green's functions Robin de Jong
6. A control theorem for the images of Galois actions on certain infinite families of modular forms Luis Dieulefait
7. Galois realizations of families of Projective Linear Groups via cusp forms Luis Dieulefait
8. A strong symmetry property of Eisenstein series Bernhard Heim
9. A conjecture on a Shimura type correspondence for Siegel modular forms, and Harder's conjecture on congruences Tomoyoshi Ibukiyama
10. Petersson's trace formula and the Hecke eigenvalues of Hilbert modular forms Andrew Knightly and Charles Li
11. Modular shadows and the Lévy-Mellin ?-adic transform Yuri I. Manin and Matilde Marcolli
12. Jacobi forms of critical weight and Weil representations Nils-Peter Skoruppa
13. Tannakian categories attached to abelian varieties Rainer Weissauer
14. Torelli's theorem from the topological point of view Rainer Weissauer
15. Existence of Whittaker models related to four dimensional symplectic Galois representations Rainer Weissauer
16. Multiplying modular forms Martin H. Weissman
17. On projective linear groups over finite fields Gabor Wiese.

Subject Areas: Number theory [PBH]