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The distribution of points on superelliptic curves over finite fields


Authors: GilYoung Cheong, Melanie Matchett Wood and Azeem Zaman
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
Published electronically: December 15, 2014
MathSciNet review: 3314052
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Abstract | References | Similar Articles | Additional Information

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.


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Additional 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
Email: mmwood@math.wisc.edu

Azeem Zaman
Affiliation: American Institute of Mathematics, 360 Portage Ave, Palo Alto, California 94306-2244

DOI: https://doi.org/10.1090/S0002-9939-2014-12218-0
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
Article copyright: © Copyright 2014 American Mathematical Society

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