Binomial convolution sum of divisor functions associated with Dirichlet character modulo 8

Abstract

In this article, we compute binomial convolution sums of divisor functions associated with the Dirichlet character modulo 8, which is the remaining primitive Dirichlet character modulo powers of 2 yet to be considered. To do this, we provide an explicit expression of a general modular form of even weight for Γ0(32){\Gamma }_{0}\left(32) in terms of its basis, and use an identity of Huard, Ou, Spearman, and Williams. As an application, we also compute the number of representations by quadratic forms under parity conditions.

Keywords

• divisor function
• dirichlet character
• convolution sum
• arithmetic identity
• eisenstein series
• 11a25
• 11e25
• 11f11
• 11f20
• 11f30