Modular Forms on Schiermonnikoog (eBook, PDF)

Redaktion: Edixhoven, Bas

• Format: PDF

Produktbeschreibung

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.

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Produktdetails

• Verlag: Cambridge University Press
• Erscheinungstermin: 27. November 2008
• Englisch
• ISBN-13: 9780511451423
• Artikelnr.: 38209651

Inhaltsangabe

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.