Arithmetic properties of L-functions attached to Hilbert modular forms | Posted on:2013-11-25 | Degree:Ph.D | Type:Thesis | University:Oklahoma State University | Candidate:Tanabe, Naomi | Full Text:PDF | GTID:2450390008972534 | Subject:Mathematics | Abstract/Summary: | | The goal of this thesis is to study some arithmetic properties of L-functions attached to Hilbert modular forms. We mainly use a representation theoretical point of view for the study, which can be done by associating Hilbert modular forms of our interests with automorphic representations of GL(2). Furthermore, their L-functions are deeply related. We use this realization to analyze the critical L-values for Hilbert modular forms, which reduces some technical difficulties.;The thesis focuses on three main theorems which concern: Algebraicity theorem; Congruence property; and Non-vanishing property. The first theorem is completed by interpreting the Mellin transform cohomologically, and the second follows from analyzing it integrally. The third theorem is obtained by studying the completed L-functions of Hilbert modular forms. | Keywords/Search Tags: | Hilbert modular forms, L-functions, Arithmetic properties, Mathematics | | Related items |
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