On the regularized imaginary doi-naganuma lifting

초록

Asai and Friedberg studied the imaginary Doi-Naganuma lifting which sends elliptic modular forms to automorphic forms over an imaginary quadratic field. In this paper we extend this lifting to weak Maass forms by using regularized integral. We construct an automorphic object with singularities on the quadratic upper half-plane H1 by the regularized theta lifting of a weak Maass form. We also give the convergence region and describe its singularity type. Finally we compute the Fourier coefficients of the lifted form explicitly and present the case of Poincar´e series as an example.

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