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.
| Identifer | oai:union.ndltd.org:purdue.edu/oai:figshare.com:article/15057609 |
| Date | 26 July 2021 |
| Creators | Razan Taha (11186268) |
| Source Sets | Purdue University |
| Detected Language | English |
| Type | Text, Thesis |
| Rights | CC BY 4.0 |
| Relation | https://figshare.com/articles/thesis/p-adic_Measures_for_Reciprocals_of_L-functions_of_Totally_Real_Number_Fields/15057609 |
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