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

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 -fold cyclic covers of the line, for any , 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 -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