On class number relations in characteristic two

Abstract

Abstract. A theorem of F. Hirzebruch relates continued fractions to class numbers of quadratic number fields. A version for function fields of odd characteristic was established by D. R. Hayes and C. D. González. We present here a complete treatment of the even charateristic theory, in particular, two class number relations involving continued fractions are derived, one of which is an analogue of the Hirzebruch relation in characteristic 2.

Average values of L-functions in characteristic two

“…The following theorem relates the class number h K of the maximal order O K to the special value of the L-function of K at s = 1. [2], Theorem 5.2.) Let K/k be quadratic of genus g. Then All the orders considered in this paper are A-orders.…”

“…The main purpose of this paper is to extend it to characteristic 2. In this case, all separable quadratic extensions are Artin-Schreier, and a detailed study of this elementary theory is given in [2]. We will briefly review this theory in next section.…”

Average values of L-series for real characters in function fields

“…Quadratic function fields of even characteristic. The theory of quadratic function fields of even characteristic was first developed in [7] and we sketch below the basics on function fields of characteristic even. Every separable quadratic extension K of k is of…”