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A Variant of Lehmer’s Conjecture, II: The CM-case
Published online by Cambridge University Press: 20 November 2018
Abstract
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.
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- Copyright © Canadian Mathematical Society 2012
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