The distribution of points on superelliptic curves over finite fields
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- by GilYoung Cheong, Melanie Matchett Wood and Azeem Zaman PDF
- Proc. Amer. Math. Soc. 143 (2015), 1365-1375 Request permission
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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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
- 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