Eisenstein Series and Convolution Sums

Zafer Selcuk Aygin

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arXiv · 1612.09054

Eisenstein Series and Convolution Sums

Zafer Selcuk Aygin

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Abstract

We compute Fourier series expansions of weight $2$ and weight $4$ Eisenstein series at various cusps. Then we use results of these computations to give formulas for the convolution sums $ \sum_{a+p b=n}\sigma(a)\sigma(b)$, $ \sum_{p_1a+p_2 b=n}\sigma(a)\sigma(b)$ and $ \sum_{a+p_1 p_2 b=n}\sigma(a)\sigma(b)$ where $p, p_1, p_2$ are primes.

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BibTeX RIS

Zafer Selcuk Aygin. 2016-12-29. Eisenstein Series and Convolution Sums. https://arxiv.org/abs/1612.09054

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