Niebur-Poincare series and traces of singular moduli

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:465

Article

关键词: Meromorphic modular forms;    Polar harmonic Maass forms;    Quadratic forms;    Traces of singular moduli;    Regularized inner products;   

DOI  :  10.1016/j.jmaa.2018.05.034

来源: Elsevier

【 摘 要 】

We compute the Fourier coefficients of analogues of Kohnen and Zagier's modular forms f(k),Delta of weight 2 and negative discriminant. These functions can also be written as twisted traces of certain weight 2 Poincare series with evaluations of Niebur-Poincare series as Fourier coefficients. This allows us to study twisted traces of singular moduli in an integral weight setting. In particular, we recover explicit series expressions for twisted traces of singular moduli and extend algebraicity results by Bengoechea to the weight 2 case. We also compute regularized inner products of these functions, which in the higher weight case have been related to evaluations of higher Green's functions at CM-points. (C) 2018 Elsevier Inc. All rights reserved.

【 授权许可】

Free