Title:  Rademacher--Carlitz Polynomials

Abstract:  We introduce and study the Rademacher--Carlitz polynomial These polynomials generalize and unify various Dedekind-like sums and polynomials; most naturally, one may view the Rademacher—Carlitz polynomial as a polynomial analogue (in the sense of Carlitz) of the Dedekind--Rademacher sum, which appears in various number-theoretic, combinatorial, geometric, and computational contexts.  Our results come in three flavors: we prove a reciprocity theorem for Rademacher--Carlitz polynomials, we show how they are the only nontrivial ingredients of integer-point transforms of any rational polyhedron P, and (if time allows) we derive a novel reciprocity theorem for Dedekind--Rademacher sums, which follows naturally from our setup.

This is joint work with Matthias Beck.