On a divisor problem related to the Epstein zeta-function

Abstract

In 1995, Sankaranarayanan studied a divisor problem related to the Epstein zeta-function. By the theory of modular forms and the Riemann zeta-function, we are able to improve his result for a number of cases.

On a divisor problem related to the Epstein zeta-function, II

“…Our method is different from [8]. First we shall establish relations between k (x) and * k (Q , x) and then deduce Theorems 1 and 2 from known O -type and Ω-type estimates for k (x).…”

“…Recently inspired by Iwaniec's book [5], Lü [8] was able to improve (1.3) for the quadratic forms of level one (see [5,Chapter 11]). These quadratic forms are defined by…”

“…Moreover we have that det(A) = 1, A is equivalent to A −1 , and the number of variables satisfies ≡ 0 (mod 8). Denote by Q the set of quadratic forms of level one with variables.…”

On a divisor problem related to the Epstein zeta-function, IV

“…In this paper, we shall continue our study on divisor problems related to the Epstein zeta-function [12,13,14]. Let 2, y := (y 1 , .…”

“…Recently inspired by Iwaniec's book [8,Chapter 11], Lü [12] noted that (1.4) can be improved for the quadratic forms of level one. These quadratic forms verify the following supplementary conditions:…”