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

Kyu Hwan Lee, Se jin Oh

Research output: Contribution to journalArticlepeer-review

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∈Z≥1, which have interest in their own rights.

Original languageEnglish
Article number108309
JournalAdvances in Mathematics
Volume401
DOIs
StatePublished - 4 Jun 2022

Keywords

  • Auto-correlation functions
  • Crystal basis
  • Sato-Tate conjecture
  • Symplectic groups

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