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A Variant of Lehmer’s Conjecture, II: The CM-case
- Source :
- Canadian Journal of Mathematics. 63:298-326
- Publication Year :
- 2011
- Publisher :
- Canadian Mathematical Society, 2011.
-
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-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 (n, a(n)) = 1, where a(n) is the n-th Fourier coefficient of a normalized Hecke eigenform f of weight 2 with rational integer Fourier coefficients and having complex multiplication.
Details
- ISSN :
- 14964279 and 0008414X
- Volume :
- 63
- Database :
- OpenAIRE
- Journal :
- Canadian Journal of Mathematics
- Accession number :
- edsair.doi...........8ca89f37708427c22424a5d2f9c8b2a6