Arithmetic on a Family of Picard Curves

Rolf-Peter Holzapfel and Florin Nicolae
Additional contact information
Rolf-Peter Holzapfel: Humboldt-Universität zu Berlin, Institut für Mathematik
Florin Nicolae: Humboldt-Universität zu Berlin, Institut für Mathematik

A chapter in Finite Fields with Applications to Coding Theory, Cryptography and Related Areas, 2002, pp 187-208 from Springer

Abstract: Abstract The L-function of the curve C a : Y 3 = X 4 - aX over an algebraic number field k which contains $${\zeta _9}: = \exp \left({ \frac{{2\pi i}}{9}} \right)$$ is the inverse of a product of six Hecke L-functions with Grössencharakter. The Euler factors at primes of good reduction are determined by means of Jacobi sums associated to certain powers of the 9-th power residue character. The number of points of C a over a finite field is given in terms of such sums. The jacobian variety of C a over the field of complex numbers has complex multiplication by the ring ℤζ9.

Keywords: Zeta Function; Finite Field; Abelian Variety; Endomorphism Ring; Exceptional Point (search for similar items in EconPapers)
Date: 2002
References: Add references at CitEc
Citations:

There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-642-59435-9_14

Ordering information: This item can be ordered from
http://www.springer.com/9783642594359

DOI: 10.1007/978-3-642-59435-9_14

Access Statistics for this chapter

More chapters in Springer Books from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().