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

  • Sanoli Gun (a1) and V. Kumar Murty (a2)

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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References

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

  • Sanoli Gun (a1) and V. Kumar Murty (a2)

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