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.
Bibliographical noteFunding Information:
The research of K.-H. Lee was partially supported by a grant from the Simons Foundation (#712100).The research of S.-j. Oh was supported by the Ministry of Education of the Republic of Korea and the National Research Foundation of Korea (NRF-2019R1A2C4069647).
© 2022 Elsevier Inc.
- Auto-correlation functions
- Crystal basis
- Sato-Tate conjecture
- Symplectic groups