Singular theta lifts and near-central special values of Rankin-Selberg L-functions

Singular theta lifts and near-central special values of Rankin-Selberg L-functions

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In this thesis we study integrals of a product of two automorphic forms of weight 2 on a Shimura curve over Q against a function on the curve with logarithmic singularities at CM points obtained as a Borcherds lift. We prove a formula relating periods of this type to a near-central special value of a Rankin-Selberg L-function. The results provide evidence for Beilinson's conjectures on special values of L-functions.

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