A remark on a conjecture of Borwein and Choi

Abstract

Abstract. We prove the remaining case of a conjecture of Borwein and Choi concerning an estimate on the square of the number of solutions to n = x 2 + Ny 2 for a squarefree integer N .

On the zeros of the Epstein zeta function

“…for any ǫ > 0. In fact, for certain quadratic forms much better results are known (see [18], [19]). Since ρ(n) ≪ r Q * (n) by (4.3), (5.21) implies that the function m(x) defined by , where n j = n j (T 0 ).…”