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arXiv · 2006.06116

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

Kyu-Hwan Lee·Se-jin Oh
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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 $m \in \mathbb Z_{\ge 1}$, which have interest in their own rights.

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Kyu-Hwan Lee, Se-jin Oh. 2020-06-10. Auto-correlation functions of Sato-Tate distributions and identities of symplectic characters. https://arxiv.org/abs/2006.06116

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