Mean values of divisors of forms $n^2+Nm^2$
Number Theory
2018-12-20 v1
Abstract
Let 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 is the divisor function. We evaluate asymptotically for several , extending earlier works of Gafurov and Yu on the case .
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