The sum of divisors of a quadratic form

• Autorzy: Lilu Zhao
• Języki publikacji: EN

Abstrakty

EN

We study the sum τ 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) = C₁X³logX + C₂X³ + O(X²log⁷X),
where C₁,C₂ are two constants. This improves upon the error term $O_ε(X^{8/3+ε})$ obtained by Guo and Zhai (2012).

Kategorie tematyczne

• 11P32: Goldbach-type theorems; other additive questions involving primes
• 11P05: Waring's problem and variants
• 11P55: Applications of the Hardy-Littlewood method

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Acta Arithmetica
• Rocznik: 2014
• Tom: 163
• Numer: 2
• Strony: 161-177

Daty

wydano

2014

Twórcy

autor

Lilu Zhao

• School of Mathematics, Hefei University of Technology, Hefei 230009, People's Republic of China

Identyfikatory

DOI

10.4064/aa163-2-6