Eisenstein Series and Convolution Sums

Zafer Selcuk Aygin

Eisenstein Series and Convolution Sums

Number Theory 2016-12-30 v1

Authors: Zafer Selcuk Aygin

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.

Keywords

eisenstein series exponential sums divisor function

Cite

@article{arxiv.1612.09054,
  title  = {Eisenstein Series and Convolution Sums},
  author = {Zafer Selcuk Aygin},
  journal= {arXiv preprint arXiv:1612.09054},
  year   = {2016}
}

Comments

14 pages

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