6533b7d6fe1ef96bd1266639

RESEARCH PRODUCT

Quotients of Fermat curves and a Hecke character

Annegret WengBert Van GeemenKenji Koike

subject

Fermat's Last TheoremDiscrete mathematicsAlgebra and Number TheoryMathematics::Number TheoryApplied MathematicsGeneral EngineeringComplex multiplicationFermat's theorem on sums of two squaresComplex multiplicationField (mathematics)Wieferich primeFermat's factorization methodHecke characterHecke charactersTheoretical Computer Sciencesymbols.namesakeJacobi sumsSimple (abstract algebra)Fermat curvessymbolsEngineering(all)Mathematics

description

AbstractWe explicitly identify infinitely many curves which are quotients of Fermat curves. We show that some of these have simple Jacobians with complex multiplication by a non-cyclotomic field. For a particular case we determine the local zeta functions with two independent methods. The first uses Jacobi sums and the second applies the general theory of complex multiplication, we verify that both methods give the same result.

yearjournalcountryeditionlanguage
2005-01-01Finite Fields and Their Applications
10.1016/j.ffa.2004.02.003http://dx.doi.org/10.1016/j.ffa.2004.02.003