Auto-correlation functions of Sato–Tate distributions and identities of symplectic characters
- 주제(키워드) Auto-correlation functions , Crystal basis , Sato-Tate conjecture , Symplectic groups
- 관리정보기술 faculty
- 등재 SCIE, SCOPUS
- OA유형 Green Submitted
- 발행기관 Academic Press Inc.
- 발행년도 2022
- 총서유형 Journal
- URI http://www.dcollection.net/handler/ewha/000000190369
- 본문언어 영어
- Published As https://doi.org/10.1016/j.aim.2022.108309
초록/요약
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. © 2022 Elsevier Inc.
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