On a polynomial reciprocity theorem of Carlitz

Abstract: Carlitz proved a powerful reciprocity theorem for generalized Dedekind-Rademacher sums. Among its many consequences was an interesting polynomial reciprocity theorem which holds under a certain restriction of its parameters. Carlitz remarked that it was unclear how this restriction could be removed. In this talk, we remove this restriction and obtain a generalization of Carlitz's polynomial reciprocity theorem.

number theory

Audience: researchers in the discipline

Combinatorial and additive number theory (CANT 2022)