L-FUNCTIONS OF ELLIPTIC CURVES AND BINARY RECURRENCES. Issue 3 (22nd March 2013) - LUCA, FLORIAN; OYONO, ROGER; YALCINER, AYNUR
Abstract: Let L(s, E)= olimits_n≥ 1 a_n n^- s be the L -series corresponding to an elliptic curve E defined over Q and u = { u_m } olimits_m≥ 0 be a nondegenerate binary recurrence sequence. We prove that if M _E is the set of n such that a_n = 0 and N _E is the subset of n M _E such that a_n = u_m holds with some integer m≥ 0, then N _E is of density 0 as a subset of M _E .