Sato–Tate distributions of twists of the Fermat and the Klein quartics
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Author(s)
Fité, Francesc
Lorenzo García, Elisa
Sutherland II, Andrew Victor
Date Issued
October 2018
Journal
Research in the Mathematical Sciences
Publisher
Springer International Publishing
Citation
Fité, Francesc, et al. “Sato–Tate Distributions of Twists of the Fermat and the Klein Quartics.” Research in the Mathematical Sciences, vol. 5, no. 4, Dec. 2018. © 2018 The Authors
Version
Final published version
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 [bar over Q]-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.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
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DOI of Published Version
https://doi.org/10.1007/s40687-018-0162-0
