| Popis: |
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. |
