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A Large Sieve Zero Density Estimate ...

Lewis, Paul Dunbar.

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A Large Sieve Zero Density Estimate for Maass Cusp Forms.

Record Type:	Electronic resources : Monograph/item
Title/Author:	A Large Sieve Zero Density Estimate for Maass Cusp Forms./
Author:	Lewis, Paul Dunbar.
Published:	Ann Arbor : ProQuest Dissertations & Theses, : 2017,
Description:	56 p.
Notes:	Source: Dissertation Abstracts International, Volume: 78-09(E), Section: B.
Contained By:	Dissertation Abstracts International78-09B(E).
Subject:	Theoretical mathematics. -
Online resource:	http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=10274166
ISBN:	9781369734355

A Large Sieve Zero Density Estimate for Maass Cusp Forms.
Lewis, Paul Dunbar.

A Large Sieve Zero Density Estimate for Maass Cusp Forms. - Ann Arbor : ProQuest Dissertations & Theses, 2017 - 56 p.

Source: Dissertation Abstracts International, Volume: 78-09(E), Section: B.

Thesis (Ph.D.)--Columbia University, 2017.

The large sieve method has been used extensively, beginning with Bombieri in 1965, to provide bounds on the number of zeros of Dirichlet L-functions near the line sigma = 1. Using the Kuznetsov trace formula and the work of Deshouillers and Iwaniec on Kloosterman sums, it is possible to derive large sieve inequalities for the Fourier coefficients of Maass cusp forms, which may then similarly be used to study the corresponding Hecke-Maass L-functions. Following an approach developed by Gallagher for Dirichlet L-functions, this thesis shows how the large sieve method may be used to prove a zero density estimate, averaged over the Laplace eigenvalues, for Maass cusp forms of weight zero for the congruence subgroup Gamma0(q) for any positive integer q..

ISBN: 9781369734355Subjects--Topical Terms:

3173530
Theoretical mathematics.

A Large Sieve Zero Density Estimate for Maass Cusp Forms.
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245 1 2 $a A Large Sieve Zero Density Estimate for Maass Cusp Forms.
260 1 $a Ann Arbor : $b ProQuest Dissertations & Theses, $c 2017
300 $a 56 p.
500 $a Source: Dissertation Abstracts International, Volume: 78-09(E), Section: B.
500 $a Adviser: Dorian Goldfeld.
502 $a Thesis (Ph.D.)--Columbia University, 2017.
520 $a The large sieve method has been used extensively, beginning with Bombieri in 1965, to provide bounds on the number of zeros of Dirichlet L-functions near the line sigma = 1. Using the Kuznetsov trace formula and the work of Deshouillers and Iwaniec on Kloosterman sums, it is possible to derive large sieve inequalities for the Fourier coefficients of Maass cusp forms, which may then similarly be used to study the corresponding Hecke-Maass L-functions. Following an approach developed by Gallagher for Dirichlet L-functions, this thesis shows how the large sieve method may be used to prove a zero density estimate, averaged over the Laplace eigenvalues, for Maass cusp forms of weight zero for the congruence subgroup Gamma0(q) for any positive integer q..
590 $a School code: 0054.
650 4 $a Theoretical mathematics. $3 3173530
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710 2 $a Columbia University. $b Mathematics. $3 1684292
773 0 $t Dissertation Abstracts International $g 78-09B(E).
790 $a 0054
791 $a Ph.D.
792 $a 2017
793 $a English
856 4 0 $u http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=10274166