Mean values of divisors of forms n²+Nm²

2018/12/19 by Peng Gao, Liangyi Zhao, Gao, Peng +1
Mathematics · #Advanced Mathematical Identities #Algebraic Geometry and Number Theory #Analytic Number Theory Research #FOS: Mathematics #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.1812.07863

openalex publication_date 2018/12/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let N be any fixed positive integer and define S_N(x)=∑_{m, n ≤ x}d(n²+Nm²), where d(n) is the divisor function. We evaluate asymptotically S_N(x) for several N, extending earlier works of Gafurov and Yu on the case N=1.

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