Sato-Tate distributions of twists of the Fermat and the Klein quartics
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Publication:2319811
DOI10.1007/S40687-018-0162-0zbMATH Open1451.11050arXiv1712.07105OpenAlexW3105346932MaRDI QIDQ2319811
Author name not available (Why is that?)
Publication date: 20 August 2019
Published in: (Search for Journal in Brave)
Abstract: We determine the limiting distribution of the normalized Euler factors of an abelian threefold A defined over a number field k when A is geometrically isogenous to the cube of a CM elliptic curve defined over k. As an application, we classify the Sato-Tate distributions of the Jacobians of twists of the Fermat and Klein quartics, obtaining 54 and 23, respectively, and 60 in total. We encounter a new phenomenon not visible in dimensions 1 or 2: the limiting distribution of the normalized Euler factors is not determined by the limiting distributions of their coefficients.
Full work available at URL: https://arxiv.org/abs/1712.07105
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