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).
Highlights
Let Fq be a finite field with q = pn elements, where p is a prime number
Let χ be an absolutely irreducible, nonsingular and projective curve defined over Fq, N
Let Nq(g) denote the maximum number of Fq-rational points among the absolutely irreducible, nonsingular and projective curves of genus g defined over Fq
Summary
In this paper we determine the number of rational places of E over P for an arbitrary positive integer k ≥ 3 under the joint condition m2 | q − 1, m3 | q − 1, . We determine the number of rational places of E over P completely for arbitrary k ≥ 3 under the condition that q − 1 = ra for some prime r using local r-adic techniques These techniques are new in application to this problem in the sense that they were not used for example in [10].
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
