FURTHER RESULTS ON FIBRE PRODUCTS OF KUMMER COVERS AND CURVES WITH MANY POINTS OVER FINITE FIELDS

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2016

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Amer inst Mathematical Sciences-aims

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Mathematics
(2000)
The Atılım University Department of Mathematics was founded in 2000 and it offers education in English. The Department offers students the opportunity to obtain a certificate in Mathematical Finance or Cryptography, aside from their undergraduate diploma. Our students may obtain a diploma secondary to their diploma in Mathematics with the Double-Major Program; as well as a certificate in their minor alongside their diploma in Mathematics through the Minor Program. Our graduates may pursue a career in academics at universities, as well as be hired in sectors such as finance, education, banking, and informatics. Our Department has been accredited by the evaluation and accreditation organization FEDEK for a duration of 5 years (until September 30th, 2025), the maximum FEDEK accreditation period achievable. Our Department is globally and nationally among the leading Mathematics departments with a program that suits international standards and a qualified academic staff; even more so for the last five years with our rankings in the field rankings of URAP, THE, USNEWS and WEBOFMETRIC.

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Abstract

We study fibre products of an arbitrary number of Kummer covers of the projective line over F-q under suitable weak assumptions. If q - 1 = r(n) 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).

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/0000-0002-1694-9283; YAYLA, Oğuz/0000-0001-8945-2780

Keywords

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

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1

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Q3

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Volume

10

Issue

1

Start Page

151

End Page

162

URI

https://doi.org/10.3934/amc.2016.10.151
 https://hdl.handle.net/20.500.14411/485

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