Auto-correlation functions of Sato-Tate distributions and identities of symplectic characters

2020/06/10 by Lee, Kyu-Hwan, Oh, Se-jin
#Combinatorics (math.CO) #FOS: Mathematics #Number Theory (math.NT) #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.2006.06116

Abstract

The Sato-Tate distributions for genus 2 curves (conjecturally) describe the statistics of numbers of rational points on the curves. In this paper, we explicitly compute the auto-correlation functions of Sato-Tate distributions for genus 2 curves as sums of irreducible characters of symplectic groups. Our computations bring about families of identities involving irreducible characters of symplectic groups Sp(2m) for all m ∈ \mathbb Z_{≥ 1}, which have interest in their own rights.

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