L-FUNCTIONS OF ELLIPTIC CURVES AND BINARY RECURRENCES

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 u = {u(m)}(m >= 0) be a nondegenerate binary recurrence sequence. We prove that if M-E is the set of n such that a(n) not equal 0 and N-E is the subset of n is an element of M-E such that vertical bar a(n)vertical bar = vertical bar u(m)vertical bar holds with some integer m >= 0, then N-E is of density 0 as a subset of M-E.