We begin a study of the Fourier Coefficients of a minimal parabolic Eisenstein distribution on the double cover of SL$(3)$ over $mathbb{Q}$. The central problem in the computation of the Fourier coefficients is a computation of certain exponential sums twisted by the splitting map $s:Gamma_1(4)
ightarrow {pm1}$, which appear after unfolding the integral defining the Fourier coefficients. In cite{M06}, Miller provides a formula for $s$; unfortunately, this formula does not appear conducive to the computation of the exponential sums; however, while considering a similar computation over number fields containing the $4$-th roots of unity, Brubaker-Bump-Friedberg-Hoffstein cite{BBFH07} successfully computed the non-degenerate Fourier coefficients of a minimal parabolic Eisenstein series using a formula for an analog of $s$ in terms of Pl"{u}cker coordinates. These coordinates are well suited to the computation of the exponential sums and so our main objective is a proof that Miller's formula for $s$ can be written in terms of Pl"{u}cker coordinates. With this new formula for $s$ we can compute the Fourier coefficients of our Eisenstein distribution. The calculations of these Fourier coefficients will be addressed in a forthcoming work.
Subject (authority = RUETD)
Topic
Mathematics
RelatedItem (type = host)
TitleInfo
Title
Rutgers University Electronic Theses and Dissertations
Identifier (type = RULIB)
ETD
Identifier
ETD_8303
PhysicalDescription
Form (authority = gmd)
electronic resource
InternetMediaType
application/pdf
InternetMediaType
text/xml
Extent
1 online resource (v, 58 p.)
Note (type = degree)
Ph.D.
Note (type = bibliography)
Includes bibliographical references
Subject (authority = ETD-LCSH)
Topic
Eisenstein series
Subject (authority = ETD-LCSH)
Topic
Number theory
Note (type = statement of responsibility)
by Edmund Karasiewicz
RelatedItem (type = host)
TitleInfo
Title
School of Graduate Studies Electronic Theses and Dissertations
Identifier (type = local)
rucore10001600001
Location
PhysicalLocation (authority = marcorg); (displayLabel = Rutgers, The State University of New Jersey)
I hereby grant to the Rutgers University Libraries and to my school the non-exclusive right to archive, reproduce and distribute my thesis or dissertation, in whole or in part, and/or my abstract, in whole or in part, in and from an electronic format, subject to the release date subsequently stipulated in this submittal form and approved by my school. I represent and stipulate that the thesis or dissertation and its abstract are my original work, that they do not infringe or violate any rights of others, and that I make these grants as the sole owner of the rights to my thesis or dissertation and its abstract. I represent that I have obtained written permissions, when necessary, from the owner(s) of each third party copyrighted matter to be included in my thesis or dissertation and will supply copies of such upon request by my school. I acknowledge that RU ETD and my school will not distribute my thesis or dissertation or its abstract if, in their reasonable judgment, they believe all such rights have not been secured. I acknowledge that I retain ownership rights to the copyright of my work. I also retain the right to use all or part of this thesis or dissertation in future works, such as articles or books.