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Mathematics, Number Theory
Abstract:
n 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.
