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

Luis Emilio Garcia

Title:
Singular theta lifts and near-central special values of Rankin-Selberg L-functions
Author(s):
Garcia, Luis Emilio
Thesis Advisor(s):
Zhang, Shou-Wu
Date:
Type:
Theses
Degree:
Ph.D., Columbia University
Department(s):
Mathematics
Persistent URL:
Abstract:
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.
Subject(s):
Mathematics
Item views
750
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Suggested Citation:
Luis Emilio Garcia, , Singular theta lifts and near-central special values of Rankin-Selberg L-functions, Columbia University Academic Commons, .

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