On average theta functions of certain quadratic forms as sums of Eisenstein series

Abstract

Let QQ be an integral positive definite quadratic form of level NN in 2k2k variables. Further, we assume that (−1)kN{\left(-1)}^{k}N is a fundamental discriminant. We express the average theta function of QQ as an explicit sum of Eisenstein series, which are Hecke eigenforms by applying Atkin-Lehner involution.

Keywords

• average theta function
• eisenstein series
• atkin-lehner involution
• 11e45
• 11f11
• 11f25
• 11f27