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Hilbert Modular Forms with Coefficients in Intersection Homology and Quadratic Base Change

Hilbert Modular Forms with Coefficients in Intersection Homology and Quadratic Base Change

by Mark Goresky and Jayce Getz
Paperback
Publication Date: 13/04/2014

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In the 1970s Hirzebruch and Zagier produced elliptic modular forms with coefficients in the homology of a Hilbert modular surface. They then computed the Fourier coefficients of these forms in terms of period integrals and L-functions. In this book the authors take an alternate approach to these theorems and generalize them to the setting of Hilbert modular varieties of arbitrary dimension. The approach is conceptual and uses tools that were not available to Hirzebruch and Zagier, including intersection homology theory, properties of modular cycles, and base change. Automorphic vector bundles, Hecke operators and Fourier coefficients of modular forms are presented both in the classical and adelic settings. The book should provide a foundation for approaching similar questions for other locally symmetric spaces.
ISBN:
9783034807951
9783034807951
Category:
Number theory
Format:
Paperback
Publication Date:
13-04-2014
Language:
English
Publisher:
Birkhauser Verlag AG
Country of origin:
Switzerland
Pages:
258
Dimensions (mm):
235x155x18mm
Weight:
0.42kg

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