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

摘要

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).