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

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ÖZBUDAK F., Temur B. G., YAYLA O.

ADVANCES IN MATHEMATICS OF COMMUNICATIONS, cilt.10, sa.1, ss.151-162, 2016 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 10 Sayı: 1
  • Basım Tarihi: 2016
  • Doi Numarası: 10.3934/amc.2016.10.151
  • Dergi Adı: ADVANCES IN MATHEMATICS OF COMMUNICATIONS
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.151-162
  • Anahtar Kelimeler: Curves with many points over finite fields, Kummer covers, fibre products, rational points, algebraic function fields, RATIONAL-POINTS
  • Orta Doğu Teknik Üniversitesi Adresli: Evet

Özet

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).