Geodesic
A Variant of Lehmer’s Conjecture, II: The CM-case
Canadian journal of mathematics, Tome 63 (2011) no. 2, pp. 298-326

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DOI

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.
DOI : 10.4153/CJM-2011-002-4
Mots-clés : 11F11, 11F30 
Gun, Sanoli; Murty, V. Kumar. A Variant of Lehmer’s Conjecture, II: The CM-case. Canadian journal of mathematics, Tome 63 (2011) no. 2, pp. 298-326. doi: 10.4153/CJM-2011-002-4
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     title = {A {Variant} of {Lehmer{\textquoteright}s} {Conjecture,} {II:} {The} {CM-case}},
     journal = {Canadian journal of mathematics},
     pages = {298--326},
     year = {2011},
     volume = {63},
     number = {2},
     doi = {10.4153/CJM-2011-002-4},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CJM-2011-002-4/}
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