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arXiv · 1211.4715

Petersson inner products of weight one modular forms

Maryna Viazovska
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Abstract

In this paper we study regularized Petersson products between a holomorphic theta series associated to a positive definite binary quadratic form and a weakly holomorphic weight 1 modular form with integral Fourier coefficients. In our recent work \cite{Via CM Green} motivated by the conjecture of B. Gross and D. Zagier on the CM values of higher Green's functions we have discovered that 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. The main result of the present paper is the explicit factorization formula for the obtained algebraic number.

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Maryna Viazovska. 2013-03-22. Petersson inner products of weight one modular forms. https://arxiv.org/abs/1211.4715

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