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1. arXiv:1603.00672 (Published 2016-03-02)

   Distribution of points on m-fold covers over finite fields

   GilYoung Cheong
   Comments: Comments are welcome!

   Categories: math.NT, math.CO

   Keywords: finite field, m-fold covers, distribution, prime power, invariant tend
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   Given a finite field F_q with a prime power q, we compute the distribution of the number of F_q-points that curves of the form y^m = f(x) take with fixed invariant of f(x), letting the invariant tend to infinity. Previously, many different authors took the invariant as genus of curves or degree of polynomials. We propose a new invariant in an attempt to generalize some of the existing works by giving a conjecture and establishing some new cases of it.

2. arXiv:1210.0456 (Published 2012-10-01)

   The distribution of points on superelliptic curves over finite fields

   GilYoung Cheong, Melanie Matchett Wood, Azeem Zaman
   Categories: math.NT

   Subjects: 11G20, 11T55, 11R58, 14H25, 11R45, 11R20, 11T06

   Keywords: distribution, smooth m-fold cyclic covers, smooth superelliptic curves, p-fold cyclic covers, limits taken differ
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   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 previous work of Kurlberg, Rudnick, Bucur, David, Feigon, and Lalin for p-fold cyclic covers, but the limits taken differ slightly and the resulting distributions are interestingly different.