The sum of divisors of a quadratic form

2014/01/10 by Zhao, Lilu
#FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1401.2310

Abstract

We study the sum of divisors of the quadratic form m₁²+m₂²+m₃². Let S₃(X)=∑_{1≤ m1,m2,m3≤ X}τ(m₁²+m₂²+m₃²). We obtain the asymptotic formula S₃(X)=C₁X³log X+ C₂X³+O(X²log⁷ X), where C₁,C₂ are two constants. This improves upon the error term O_ε(X^8/3+ε) obtained by Guo and Zhai.

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