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

초록

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 Γ 0 (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. © 2024 the author(s), published by De Gruyter.

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