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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 
 

 

Sato-Tate distributions on Abelian surfaces


Author: Noah Taylor
Journal: Trans. Amer. Math. Soc. 373 (2020), 3541-3559
MSC (2010): Primary 11F41, 11M45
DOI: https://doi.org/10.1090/tran/8025
Published electronically: February 20, 2020
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Abstract: We prove a few new cases of the Sato-Tate conjecture, using a new automorphy theorem of Allen et al. Then, in the unproven cases, we use partial results to describe nontrivial asymptotics on the trace of Frobenius, and prove their optimality given current knowledge.


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Additional Information

Noah Taylor
Affiliation: Department of Mathematics, University of Chicago, Chicago, Illinois 60637
Email: noaht@uchicago.edu

DOI: https://doi.org/10.1090/tran/8025
Received by editor(s): February 17, 2019
Received by editor(s) in revised form: July 2, 2019, and September 4, 2019
Published electronically: February 20, 2020
Additional Notes: The author was supported in part by NSF Grant DMS-$1701703$.
Article copyright: © Copyright 2020 American Mathematical Society