We 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.

Quotients of Fermat curves and a Hecke character / B. van Geemen, K. Koike, A. Weng. - In: FINITE FIELDS AND THEIR APPLICATIONS. - ISSN 1071-5797. - 11:1(2005), pp. 6-29.

Quotients of Fermat curves and a Hecke character

B. van Geemen
Primo
;
2005

Abstract

We 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.
Fermat curves ; Complex multiplication ; Jacobi sums ; Hecke characters
Settore MAT/03 - Geometria
2005
Article (author)
File in questo prodotto:
Non ci sono file associati a questo prodotto.
Pubblicazioni consigliate

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2434/34933
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 4
  • ???jsp.display-item.citation.isi??? 3
social impact