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Three-term theorems for Dedekind-like sums

MSRI-UP 2012: Enumerative Combinatorics June 16, 2012 - July 29, 2012

July 29, 2012 (10:00 AM PDT - 11:00 AM PDT)
Speaker(s): Jordan Clark, Stefan Klajbor, Chelsie Norton
Location: MSRI: Baker Board Room
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Abstract

Dedekind sums are finite arithmetic sums with many applications in number theory, discrete geometry, topology, computer science, and other areas. (For an introduction see, e.g., Chapter 8 in this book.)A famous paper by J. Pommersheim contains a three-term reciprocity law for the classical Dedekind sum. K. Girstmair explained Pommersheim's theorem by proving a link to two older theorems of Dedekind and Rademacher. There are many generalizations of Dedekind sums (some families are summarized here and here); the goal of our project is to find analogues of Pommersheim's three-term theorem for these generalizations, such as the three term theorem by M. Beck, C. Haase, and A. Matthews.

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