Modular Forms on Schiermonnikoog

Bas Edixhoven is a professor in the Mathematical Institute at Leiden University, Netherlands. Gerard van der Geer is Professor of Algebra in the Korteweg-de Vries Institute for Mathematics at the University of Amsterdam. Ben Moonen is a professor in the Korteweg-de Vries Institute for Mathematics at the University of Amsterdam.

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

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.