By Jayce Getz,Mark Goresky

within the Nineteen Seventies Hirzebruch and Zagier produced elliptic modular kinds with coefficients within the homology of a Hilbert modular floor. They then computed the Fourier coefficients of those kinds by way of interval integrals and L-functions. during this ebook the authors take another method of those theorems and generalize them to the atmosphere of Hilbert modular sorts of arbitrary size. The method is conceptual and makes use of instruments that weren't on hand to Hirzebruch and Zagier, together with intersection homology thought, homes of modular cycles, and base switch. Automorphic vector bundles, Hecke operators and Fourier coefficients of modular types are provided either within the classical and adèlic settings. The booklet may still offer a starting place for forthcoming related questions for different in the neighborhood symmetric spaces.

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Hilbert Modular Forms with Coefficients in Intersection Homology and Quadratic Base Change: 298 (Progress in Mathematics) by Jayce Getz,Mark Goresky

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