Analogies of Dedekind sums in function fields

Abstract

Listen

Translate article

The classical Dedekind sums were found in transformation formulae of η-functions. It is known that these sums have some properties, especially a reciprocity law s ( a , c ) + s ( c , a ) = a 2 + c 2 − 3 a c + 1 12 a c . Sczech (1984) [5] expanded his theory for analogies of Dedekind sums and log | η ( z ) | in imaginary quadratic fields. And in my paper [6] (Okada, 1989) we studied analogies of Dedekind sums in function fields. In this paper we correct some mistakes, change some notations and rewrite some lines in the previous paper. And also in this paper we consider another analogies of Dedekind sums and a reciprocity law for these Dedekind sums.