Power residues of Fourier coefficients of elliptic curves with complex multiplication

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dc.creatorWeston, Tom
dc.creatorZaurova, Elena
dc.date2006-04-03
dc.date.accessioned2026-07-07T07:10:26Z
dc.date.available2026-07-07T07:10:26Z
dc.descriptionFix m >= 1 and let E be an elliptic curve over Q with complex multiplication. We formulate conjectures on the density of primes p (congruent to one modulo m) for which the pth Fourier coefficient of E is an mth power modulo p; often these densities differ from the naive expectation of 1/m. We also prove our conjectures for m dividing the number of roots of unity lying in the CM field of E; the most involved case is m=4 and complex multiplication by Q(i).
dc.identifierhttps://arxiv.org/abs/math/0604034
dc.identifierhttp://arxiv.org/abs/math/0604034
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/111421
dc.subjectNumber Theory
dc.subject11F30; 11G15
dc.titlePower residues of Fourier coefficients of elliptic curves with complex multiplication
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