Title: Moments of the error term in the Sato-Tate law for elliptic curves
Speaker: Stephan Baier (RKMVU, Belur)
Date: 27 August 2018
Time: 3 pm
Venue: LH-1, Mathematics Department
This is joint work with N. Prabhu (IISER Pune). We derive new bounds for moments of the error in the Sato-Tate law over families of elliptic curves. As applications, we deduce new almost-all results for the said errors and a conditional Central Limit Theorem on the distribution of these errors. Our method builds on recent work by N. Prabhu and K. Sinha who derived a Central Limit Theorem on the distribution of the errors in the Sato-Tate law for families of cusp forms for the full modular group. In addition, identities by Birch and Melzak play a crucial rule in this paper. Birch’s identities connect moments of coefficients of Hasse-Weil L-functions for elliptic curves with the Kronecker class number and further with traces of Hecke operators. Melzak’s identity is combinatorial in nature.