Fibre products of Kummer covers and curves with many points (original) (raw)

Abstract

We study the general fibre product of any two Kummer covers of the projective line over finite fields. Under some assumptions, we obtain an involved condition for the existence of rational points in the fibre product over a rational point of the projective line so that we determine the exact number of the rational points. Using this, we construct explicit examples of such fibre products with many rational points. In particular we obtain a record and a new entry for the table (http://www.science.uva.nl/\~geer/tables-mathcomp15.ps).

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Authors and Affiliations

1. Department of Mathematics, Middle East Technical University, İnönü Bulvarı, 06531, Ankara, Turkey
   Ferruh Özbudak
2. Department of Mathematics, Atılım University, İncek, Gölbaşı, 06836, Ankara, Turkey
   Burcu Gülmez Temur

Authors

1. Ferruh Özbudak
2. Burcu Gülmez Temur

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Correspondence toFerruh Özbudak.

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Özbudak, F., Temur, B.G. Fibre products of Kummer covers and curves with many points.AAECC 18, 433–443 (2007). https://doi.org/10.1007/s00200-007-0047-8

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• Received: 11 August 2005
• Revised: 29 November 2006
• Published: 30 June 2007
• Issue date: October 2007
• DOI: https://doi.org/10.1007/s00200-007-0047-8

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Mathematics Subject Classification (2000)