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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2024 MCQ for Proceedings of the American Mathematical Society is 0.85.

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The distribution of points on superelliptic curves over finite fields
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by GilYoung Cheong, Melanie Matchett Wood and Azeem Zaman
Proc. Amer. Math. Soc. 143 (2015), 1365-1375
DOI: https://doi.org/10.1090/S0002-9939-2014-12218-0
Published electronically: December 15, 2014

Abstract:

We give the distribution of points on smooth superelliptic curves over a fixed finite field, as their degree goes to infinity. We also give the distribution of points on smooth $m$-fold cyclic covers of the line, for any $m$, as the degree of their superelliptic model goes to infinity. This builds on the previous work of Kurlberg, Rudnick, Bucur, David, Feigon, and Lalín for $p$-fold cyclic covers, but the limits taken differ slightly and the resulting distributions are interestingly different.
References
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Bibliographic Information
  • GilYoung Cheong
  • Affiliation: Department of Mathematics, University of Wisconsin-Madison, 480 Lincoln Drive, Madison, Wisconsin 53705
  • Melanie Matchett Wood
  • Affiliation: Department of Mathematics, University of Wisconsin-Madison, 480 Lincoln Drive, Madison, Wisconsin 53705
  • MR Author ID: 709533
  • Email: mmwood@math.wisc.edu
  • Azeem Zaman
  • Affiliation: American Institute of Mathematics, 360 Portage Ave, Palo Alto, California 94306-2244
  • Received by editor(s): October 1, 2012
  • Received by editor(s) in revised form: February 14, 2013
  • Published electronically: December 15, 2014
  • Communicated by: Matthew A. Papanikolas
  • © Copyright 2014 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 143 (2015), 1365-1375
  • MSC (2010): Primary 11G20, 11R45, 11R58, 11T55, 14H25; Secondary 11G25, 11R20, 11T06
  • DOI: https://doi.org/10.1090/S0002-9939-2014-12218-0
  • MathSciNet review: 3314052