Overview

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 adèlic settings. The book should provide a foundation for approaching similar questions for other locally symmetric spaces.

Full Product Details

Author:   Jayce Getz ,  Mark Goresky
Publisher:   Birkhauser Verlag AG
Imprint:   Birkhauser Verlag AG
Edition:   2012 ed.
Volume:   298
Dimensions:   Width: 15.50cm , Height: 1.80cm , Length: 23.50cm
Weight:   0.421kg
ISBN:  

9783034807951

ISBN 10:   3034807953
Pages:   258
Publication Date:   13 April 2014
Audience:   Professional and scholarly ,  Professional & Vocational
Format:   Paperback
Publisher's Status:   Active
Availability:   Manufactured on demand  
We will order this item for you from a manufactured on demand supplier.

Table of Contents

Chapter 1. Introduction.- Chapter 2. Review of Chains and Cochains.- Chapter 3. Review of Intersection Homology and Cohomology.- Chapter 4. Review of Arithmetic Quotients.- Chapter 5. Generalities on Hilbert Modular Forms and Varieties.- Chapter 6. Automorphic vector bundles and local systems.- Chapter 7. The automorphic description of intersection cohomology.- Chapter 8. Hilbert Modular Forms with Coefficients in a Hecke Module.- Chapter 9. Explicit construction of cycles.- Chapter 10. The full version of Theorem 1.3.- Chapter 11. Eisenstein Series with Coefficients in Intersection Homology.- Appendix A. Proof of Proposition 2.4.- Appendix B. Recollections on Orbifolds.- Appendix C. Basic adèlic facts.- Appendix D. Fourier expansions of Hilbert modular forms.- Appendix E. Review of Prime Degree Base Change for GL2.- Bibliography.

Reviews

Author Information

Tab Content 6

Author Website:  

Customer Reviews

Recent Reviews

No review item found!

Add your own review!

Countries Available

All regions