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The minimal parabolic Eisenstein distribution on the double cover of SL(3) over Q
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Karasiewicz, Edmund. The minimal parabolic Eisenstein distribution on the double cover of SL(3) over Q. Retrieved from https://doi.org/doi:10.7282/T32R3VS3

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TitleThe minimal parabolic Eisenstein distribution on the double cover of SL(3) over Q
NameKarasiewicz, Edmund (author); Miller, Stephen D (chair); Iwaniec, Henryk (internal member); Kontorovich, Alex (internal member); Chinta, Gautam (outside member); Rutgers University; School of Graduate Studies
Date Created2017
Other Date2017-10 (degree)
SubjectMathematics, Eisenstein series, Number theory
Extent1 online resource (v, 58 p.)
DescriptionWe 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.
NotePh.D.
NoteIncludes bibliographical references
Noteby Edmund Karasiewicz
Genretheses, ETD doctoral
Persistent URLhttps://doi.org/doi:10.7282/T32R3VS3
Languageeng
CollectionSchool of Graduate Studies Electronic Theses and Dissertations
Organization NameRutgers, The State University of New Jersey
RightsThe author owns the copyright to this work.
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