Evaluation of Some Convolution Sums by Quasimodular Forms

Authors

  • Baris Kendirli Fatih University

Keywords:

Quasimodular forms, divisor functions, convolution sums, representation number 11A25, 11F11, 11F25, 11F20

Abstract

We evaluate the convolution sums ∑_{l+135m=n}σ(l)σ(m),  ∑_{3l+45m=n}σ(l)σ(m),  ∑_{5l+27m=n}σ(l)σ(m),∑_{9l+15m=n}σ(l)σ(m), ∑_{l+45m=n}σ(l)σ(m),∑_{5l+9m=n}σ(l)σ(m), and ∑_{3l+15m=n}σ(l)σ(m) for all nεN using the theory of quasimodular forms and use some of these convolution sums to determine the number of representations of a positive integer n by some direct sum of the forms x₲+xâ‚xâ‚‚+34x₂²,5x₲+5xâ‚xâ‚‚+8x₂²,4x₲±3xâ‚xâ‚‚+9x₂², 2x₲±xâ‚xâ‚‚+17x₂² of discriminant -135

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Published

2015-01-29

Issue

Vol. 8 No. 1: (January 2015)

Section

Number Theory

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How to Cite

Evaluation of Some Convolution Sums by Quasimodular Forms. (2015). European Journal of Pure and Applied Mathematics, 8(1), 81-110. https://www.ejpam.com/index.php/ejpam/article/view/2289