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

Kyu Hwan Lee; Se jin Oh

doi:10.1016/j.aim.2022.108309

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

Kyu Hwan Lee, Se jin Oh

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

2 Scopus citations

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 language	English
Article number	108309
Journal	Advances in Mathematics
Volume	401
DOIs	https://doi.org/10.1016/j.aim.2022.108309
State	Published - 4 Jun 2022

Bibliographical note

Funding 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).

Publisher Copyright:
© 2022 Elsevier Inc.

Keywords

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

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10.1016/j.aim.2022.108309

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

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AU - Oh, Se jin

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N2 - 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.

AB - 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.

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KW - Crystal basis

KW - Sato-Tate conjecture

KW - Symplectic groups

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JO - Advances in Mathematics

JF - Advances in Mathematics

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ER -

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

Abstract

Bibliographical note

Keywords

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