PurdueThesis_Taha (2).pdf (470.52 kB)

p-adic Measures for Reciprocals of L-functions of Totally Real Number Fields

Download (470.52 kB)
thesis
posted on 26.07.2021, 23:58 by Razan TahaRazan Taha
We generalize the work of Gelbart, Miller, Pantchichkine, and Shahidi on constructing p-adic measures to the case of totally real fields K. This measure is the Mellin transform of the reciprocal of the p-adic L-function which interpolates the special values at negative integers of the Hecke L-function of K. To define this measure as a distribution, we study the non-constant terms in the Fourier expansion of a particular Eisenstein series of the Hilbert modular group of K. Proving the distribution is a measure requires studying the structure of the Iwasawa algebra.

History

Degree Type

Doctor of Philosophy

Department

Mathematics

Campus location

West Lafayette

Advisor/Supervisor/Committee Chair

Freydoon Shahidi

Additional Committee Member 2

David Goldberg

Additional Committee Member 3

Baiying Liu

Additional Committee Member 4

Tong Liu