\(L\)-functions of elliptic curves and binary recurrences

Authors

  • F. Luca UNAM
  • R. Oyono Universite de la Polynesie Francaise
  • A. Yalciner Selcuk University

Keywords:

L-functions of elliptic curves, binary recurrences

Abstract

Let $L(s,E)=\sum_{n\ge 1} a_n n^{-s}$ be the $L$-series corresponding to an elliptic curve $E$ defined over $\Q$ and ${\bf u}=\{u_m\}_{m\ge 0}$ be a non degenerate binary recurrence sequence. We prove that if ${\mathcal M}_E$ is the set of $n$ such that $a_n\ne 0$ and ${\mathcal N}_E$ is the subset of $n\in {\mathcal M}_E$ such that $|a_n|=|u_m|$ holds with some integer $m\ge 0$, then ${\mathcal N}_E$ is of density $0$ as a subset of ${\mathcal M}_E$. 10.1017/S0004972713000166

Published

2013-09-27

Issue

Vol. 88 No. 3 (2013)

Section

Articles
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