Explicit differentiation of totally real p-adic Hecke L-functions
Dr. Luochen Zhao
2023-11-17 11:00-12:00
MCM110
Speaker: Dr. Luochen Zhao (Hebrew University of Jerusalem)Time: 11:00-12:00 November 17, 2023 (Friday)
Place: MCM110
Title: Explicit differentiation of totally real p-adic Hecke L-functions
Abstract: The leading term of the p-adic Hecke L-function of a totally real field is of arithmetic interest by the Gross--Stark conjecture, known by the works of Darmon--Dasgupta--Pollack and Dasgupta--Kakde--Ventullo. When the field is Q, this is witnessed by the combination of the Ferrero--Greenberg formula that relates derivatives to Morita Gamma values and the Gross--Koblitz formula that relates Gamma values to Gauss sums. In this talk I'll report my generalization of the Ferrero--Greenberg formula to the totally real case using the infinite sum expression of the p-adic L-function after Delbourgo.
