Type: Article

Squares in a certain sequence related to L-functions of elliptic curves

Luca, Florian; Yalciner, Aynur;

Abstract:

Let L(s, E) = Sigma(n >= 1) a(n)n(-s) be the L-series corresponding to an elliptic curve E defined over Q and satisfying certain technical conditions. We prove that the set of positive integers n such that n(2) - a(n2) + 1 = square has asymptotic density 0. (C) 2013 Elsevier Inc. All rights reserved.