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 varieties by way of interval integrals and L-functions. during this publication the authors take an alternative method of those theorems and generalize them to the surroundings of Hilbert modular types of arbitrary size. The process is conceptual and makes use of instruments that weren't to be had to Hirzebruch and Zagier, together with intersection homology concept, houses of modular cycles, and base switch. Automorphic vector bundles, Hecke operators and Fourier coefficients of modular kinds are offered either within the classical and adèlic settings. The publication may still supply a origin for coming near near comparable questions for different in the neighborhood symmetric areas.
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