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Birkhäuser - Birkhäuser Mathematics | Hilbert Modular Forms with Coefficients in Intersection Homology and Quadratic Base Change

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

Series: Progress in Mathematics, Vol. 298

Getz, Jayce, Goresky, Mark

2012, XIV, 258 p.

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  • Award winning monograph of the 2011 Ferran Sunyer i Balaguer Prize competition
  • Contains basic material on intersection cohomology, modular cycles and automorphic forms from the classical and adèlic points of view
  •  Appendices on orbifolds, Fourier expansions, and base change help to make the book self-contained
  • Contains topics of interest for geometers and number theorists interested in locally symmetric spaces and automorphic forms

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.

Content Level » Research

Keywords » Fourier coefficients - Hecke operators - Hilbert modular varieties - automorphic forms - intersection cohomology

Related subjects » Birkhäuser Mathematics

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