A Variant of Lehmer’s Conjecture, II: The CM-case

Gun, Sanoli ; Murty, V. Kumar

Canadian journal of mathematics, Tome 63 (2011) no. 2, pp. 298-326

Résumé

Let $f$ be a normalized Hecke eigenform with rational integer Fourier coefficients. It is an interesting question to know how often an integer $n$ has a factor common with the $n\text{-th}$ Fourier coefficient of $f$ . It has been shown in previous papers that this happens very often. In this paper, we give an asymptotic formula for the number of integers $n$ for which $\left( n,\,a\left( n \right) \right)\,=\,1$ , where $a\left( n \right)$ is the $n\text{-th}$ Fourier coefficient of a normalized Hecke eigenform $f$ of weight 2 with rational integer Fourier coefficients and having complex multiplication.

Détail

DOI : 10.4153/CJM-2011-002-4

Mots-clés : 11F11, 11F30

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