Modular Forms on Schiermonnikoog

ISBN-13: 9780521493543 / Angielski / Twarda / 2008 / 360 str.

Opis

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.

Spis treści

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.