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Modular Forms on Schiermonnikoog Bas Edixhoven (Universiteit Leiden)

Modular Forms on Schiermonnikoog By Bas Edixhoven (Universiteit Leiden)

Modular Forms on Schiermonnikoog by Bas Edixhoven (Universiteit Leiden)


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Summary

Presents the state of the art in a range of topics such as Siegel modular forms, Hecke eigenvalues of Hilbert modular forms, Weil representations, Tannakian categories and Torelli's theorem. Ideal for all researchers and graduate students working on modular forms and related areas of number theory and algebraic geometry.

Modular Forms on Schiermonnikoog Summary

Modular Forms on Schiermonnikoog by Bas Edixhoven (Universiteit Leiden)

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.

About Bas Edixhoven (Universiteit Leiden)

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.

Table of Contents

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 Boecherer, 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 Levy-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.

Additional information

NPB9780521493543
9780521493543
0521493544
Modular Forms on Schiermonnikoog by Bas Edixhoven (Universiteit Leiden)
New
Hardback
Cambridge University Press
2008-11-27
360
N/A
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