Traces of CM values of modular functions

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Zagier proved that the traces of singular moduli, i.e., the sums of the values of the classical j-invariant over quadratic irrationalities, are the Fourier coefficients of a modular form of weight 3/2 with poles at the cusps. Using the theta correspondence, we generalize this result to traces of CM values of (weakly holomorphic) modular functions on modular curves of arbitrary genus. We also study the theta lift for the weight 0 Eisenstein series for SL(2,Z) and realize a certain generating series of arithmetic intersection numbers as the derivative of Zagier's Eisenstein series of weight 3/2. This recovers a result of Kudla, Rapoport and Yang.
29 pages

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Number Theory, Algebraic Geometry, 11F11, 11F30

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http://salesiana.dossiersoluciones.com/handle/123456789/72314

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0408406
 http://arxiv.org/abs/math/0408406

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arXiv