Full Record

Author | File, Daniel Whitman |

Title | On the degree 5 L-function for GSp(4) |

URL | http://rave.ohiolink.edu/etdc/view?acc_num=osu1279567891 |

Publication Date | 2010 |

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 |

Sample Search Hits | Sample Images

…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…