Can I read Densities for 4-Class Ranks of Quadratic Function Fields on EtoBox?

Densities for 4-Class Ranks of Quadratic Function Fields by Christian Wittmann is a Mathematics article available to read on EtoBox.

What is Densities for 4-Class Ranks of Quadratic Function Fields about?

Let F = F q (T ) be a rational function field of odd characteristic, and fix a positive integer t. In this article we study the family of quadratic function fields K = F ( √ D ), where D is a polynomial over F q of odd degree having t distinct irreducible factors. The 4class rank r 4 (K ) is the rank of the 4-torsion of the group of divisor classes of K , and it is known that 0 r 4 (K ) t -1. For fixed r we compute the proportion of such fields K satisfying r 4 (K ) = r, and in particular we determine the behaviour of this value as t → ∞. We will need some asymptotic results for these computations, in particular the number of polynomials D as above whose irreducible factors fulfill certain parity and quadratic residue conditions.

Who reads Densities for 4-Class Ranks of Quadratic Function Fields?

Author

Christian Wittmann

Publisher

Elsevier Science; Elsevier ; Elsevier Inc.; Elsevier BV (ISSN 0022-314X)

Published

2009

Language

EN

Field

Mathematics (Physical Sciences)