Finite Number of Fibre Products of Kummer Covers and Curves With Many Points Over Finite Fields

Abstract

We study fibre products of a finite number of Kummer covers of the projective line over finite fields. We determine the number of rational points of the fibre product over a rational point of the projective line, which improves the results of Ozbudak and Temur (Appl Algebra Eng Commun Comput 18:433-443, 2007) substantially. We also construct explicit examples of fibre products of Kummer covers with many rational points, including a record and two new entries for the current table (http://www.manypoints.org, 2011).