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 includingHilbert 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. Collection of articles by leaders in the field; presents the state of the art in modular forms. Topics covered include Siegel modular forms, Hecke eigenvalues of Hilbert modular forms, Weil representations, Tannakian categories and Torelli's theorem. Ideal for academic researchers and graduate students in number theory and algebraic geometry; string theorists will alsofind the collection of interest INDICE: Preface; Contributors; 1. Modular forms Bas Edixhoven, Gerard van der Geer and Ben Moonen; 2. On the basis problem for Siegel modular forms withlevel 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 oncertain 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 andthe Hecke eigenvalues of Hilbert modular forms Andrew Knightly and Charles Li; 11. Modular shadows and the Lévy-Mellin 8-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 formsMartin H. Weissman; 17. On projective linear groups over finite fields Gabor Wiese
- ISBN: 978-0-521-49354-3
- Editorial: Cambridge University
- Encuadernacion: Cartoné
- Páginas: 360
- Fecha Publicación: 27/11/2008
- Nº Volúmenes: 1
- Idioma: Inglés