Further results on fibre products of Kummer covers and curves with many points over finite fields

Ferruh  Özbudak; Burcu Gülmez  Temür; Oǧuz  Yayla

doi:10.3934/amc.2016.10.151

Article Contents

2016, Volume 10, Issue 1: 151-162. Doi: 10.3934/amc.2016.10.151

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Further results on fibre products of Kummer covers and curves with many points over finite fields

1.
Department of Mathematics and Institute of Applied Mathematics, Middle East Technical University, Dumlupnar Bulvar, 06800, Ankara
2.
Department of Mathematics, Atlm University, Incek, Golbas, 06836, Ankara
3.
Department of Mathematics, Hacettepe University, Beytepe, 06800, Ankara

Received: November 30, 2014

Revised: November 30, 2015

Published: January 2016

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Abstract

We study fibre products of an arbitrary number of Kummer covers of the projective line over $\mathbb{F}_q$ under suitable weak assumptions. If $q-1 = r^a$ for some prime $r$, then we completely determine the number of rational points over a rational point of the projective line. Using this result we obtain explicit examples of fibre products of three Kummer covers supplying new entries for the current table of curves with many points (http://www.manypoints.org, October 31 2015).

Keywords:

Curves with many points over finite fields,
Kummer covers,
fibre products,
rational points,
algebraic function fields.

Mathematics Subject Classification: Primary: 11G20, 14G15; Secondary: 14H25.

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References

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