[Geom.,Alg.&Phys.] Auto-correlation functions of Sato-Tate distributions and identities of symplectic characters
ABSTRACT
The Sato--Tate distributions for genus 2 curves describe the statistics of the numbers of rational points on these curves. In this talk, we explicitly compute the autocorrelation functions of Sato--Tate distributions for genus 2 curves as sums of irreducible characters of symplectic groups. Our computations yield families of identities involving irreducible characters of the symplectic groups Sp(2m) for all m, which are of independent interest. The proofs use combinatorial objects, in particular crystals. This is a joint work with Se-jin Oh. (Zoom: Meeting ID: 811 9263 1241, Passcode: 047201, link: https://kias-re-kr.zoom.us/j/81192631241?pwd=Ihc1VK2NG3pGRHygrOJG5DQwBreC0Q.1) (https://sites.google.com/view/gapkias)
