English

Mean values of divisors of forms $n^2+Nm^2$

Number Theory 2018-12-20 v1

Abstract

Let NN be any fixed positive integer and define \begin{align*} S_N(x)=\sum_{m, n \leq x}d(n^2+Nm^2), \end{align*} where d(n)d(n) is the divisor function. We evaluate asymptotically SN(x)S_N(x) for several NN, extending earlier works of Gafurov and Yu on the case N=1N=1.

Keywords

Cite

@article{arxiv.1812.07863,
  title  = {Mean values of divisors of forms $n^2+Nm^2$},
  author = {Peng Gao and Liangyi Zhao},
  journal= {arXiv preprint arXiv:1812.07863},
  year   = {2018}
}

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18 pages