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Title On the degree 5 L-function for GSp(4)
Publication Date
Degree PhD
Discipline/Department Mathematics
Degree Level doctoral
University/Publisher The Ohio State University
Abstract In this dissertation I establish a new integral representation for the degree five L-function for the group GSp<sub>4</sub>. Let F be a number field and π an automorphic represenation of GSp<sub>4</sub>(픸<sub>F</sub>). Suppose there is an automorphic form φ ∈ V<sub>π</sub> that has a non-zero Bessel coefficient corresponding to an anisotropic binary quadratic form over F. Such coefficients generate a unique model for the representation. Then the integral computes the partial L-function for π.
Subjects/Keywords Mathematics; automorphic forms; representation theory; number theory
Contributors Cogdell, James (Advisor)
Language en
Rights unrestricted ; This thesis or dissertation is protected by copyright: all rights reserved. It may not be copied or redistributed beyond the terms of applicable copyright laws.
Country of Publication us
Format application/pdf
Record ID oai:etd.ohiolink.edu:osu1279567891
Repository ohiolink
Date Indexed 2021-01-29
Grantor The Ohio State University

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…CHAPTER 1 INTRODUCTION 1.1 Motivation In the nineteen-seventies Robert Langlands proposed several conjectures relating automorphic representation theory to number theory [25]. Langlands made use of an analytic invariant, the L-function…

…to connect number theoretic objects to automorphic representations. One method of studying automorphic L-functions is by means of an integral formula, or as it is commonly called, an integral representation. When an integral representation is…

…to give L-function criteria for lifting automorphic representations to another group [21, 42]. In certain instances the analytic properties of an L-function determine whether it is the L-function of an automorphic representation. Such a…

…Fourier coefficients of a cuspidal modular 1 form. Jacquet and Langlands were the first to prove a converse theorem in the language of automorphic representations – this type of converse theorem determines when a representation π = ⊗v πv of an adelic…

…ϕ(g)| det(g)| dg t −1 g GL2 (F )\GL2 (A) (1.12) where ϕ is a GL2 (A) automorphic form. This integral gives a heuristic for how to approach an adelic, representation theoretic version…

…unique model plays an 5 important role in representation theoretic converse theorems. It allows one to embed an abstract representation in the space of automorphic forms. 1.3 The Degree Five L-function In [1] Andrianov and Kalinin establish…

…and a functional equation. Piatetski-Shapiro and Rallis [30] adapted Andrianov’s integral representation to the setting of automorphic representations. Their integral representation is unusual in the sense that it does not involve a unique…

…five Lfunction for GSp4 . In some sense it is a refinement of [30]. The integral I consider involves the Bessel model for GSp4 which is unique. 1.4 Summary of Results Let π be an automorphic representation of GSp4 (A), φ ∈ Vπ , ν…