Petersson inner products of weight-one modular forms

Abstract

Abstract In this paper we study the regularized Petersson product between a holomorphic theta series associated to a positive definite binary quadratic form and a weakly holomorphic weight-one modular form with integral Fourier coefficients. In [18], we proved that these Petersson products posses remarkable arithmetic properties. Namely, such a Petersson product is equal to the logarithm of a certain algebraic number lying in a ring class field associated to the binary quadratic form. A similar result was obtained independently using a different method by W. Duke and Y. Li [5]. The main result of this paper is an explicit factorization formula for the algebraic number obtained by exponentiating a Petersson product.

Locations

• arXiv (Cornell University) - View - PDF
• MPG.PuRe (Max Planck Society) - View - PDF
• Journal für die reine und angewandte Mathematik (Crelles Journal) - View