AN APPLICATION OF BINARY QUADRATIC FORMS OF DISCRIMINANT TO MODULAR FORMS

Author:

AYGIN ZAFER SELCUKORCID,WILLIAMS KENNETH S.ORCID

Abstract

AbstractIn this note, we use Dedekind’s eta function to prove a congruence relation between the number of representations by binary quadratic forms of discriminant $-31$ and Fourier coefficients of a weight $16$ cusp form. Our result is analogous to the classical result concerning Ramanujan’s tau function and binary quadratic forms of discriminant $-23$ .

Publisher

Cambridge University Press (CUP)

Subject

General Mathematics

Reference5 articles.

1. On the number of representations of n by ax2+bxy+cy2

2. Ramanujan identities and Euler products for a type of Dirichlet series

3. Congruence Properties of Ramanujan's Function τ(n )

4. [1] Ciolan, A. , Languasco, A. and Moree, P. , ‘Landau and Ramanujan approximations for divisor sums and coefficients of cusp forms’, Preprint, 2021, arXiv:2109.03288, 43 pages.

Cited by 1 articles. 订阅此论文施引文献 订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献

1. Landau and Ramanujan approximations for divisor sums and coefficients of cusp forms;Journal of Mathematical Analysis and Applications;2023-03

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