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Project Information

SPECTRAL METHODS, L-FUNCTIONS AND PRIMES

Agency:
NSF

National Science Foundation

Project Number:
1101574
Contact PI / Project Leader:
IWANIEC, HENRYK
Awardee Organization:
RUTGERS THE ST UNIV OF NJ NEW BRUNSWICK

Description

Abstract Text:
The spectral methods of automorhpic forms are basic tools of analytic number theory for more than three decades. Recently new possibilities have been opened in the area of metaplectic forms. The Proposal offers to make substantial expansion of the classical results to this territory, such as for example the large sieve for cusp forms. Applications of the spectral theory of metaplectic forms to the distribution of roots of quadratic congruences are in progress. Here the point is that the resulting estimates are valid in great uniformity with respect to the discriminant. Less direct, yet motivating are applications of spectral estimates in conjunction with sieve methods to the distribution of prime numbers. In particular these could yield a very good bound for the first prime which splits completely in the Hilbert class field.

The proposal also includes (jointly with B. Conrey and K. Soundararajan) study of zeros of L-functions, proving that a respectful percentage of such zeros lay on the critical line. This very basic problem (a progress towards the celebrated Riemann Hypothesis) will definitely attract graduate students. An interaction of the PI in the related research with students and postdoc is an indispensable part of the activity under the Proposal. In fact a current student Jorge Cantillo at Rutgers already began to work on improving the density theorems for the zeros of automorphic L-functions.
Project Terms:
Area; density; graduate student; improved; Methods; Plant Roots; Postdoctoral Fellow; Research; Students; theories; tool; Work

Details

Contact PI / Project Leader Information:
Name:  IWANIEC, HENRYK
Other PI Information:
Not Applicable
Awardee Organization:
Name:  RUTGERS THE ST UNIV OF NJ NEW BRUNSWICK
City:  NEW BRUNSWICK    
Country:  UNITED STATES
Congressional District:
State Code:  NJ
District:  06
Other Information:
Fiscal Year: 2011
Award Notice Date: 18-Apr-2011
DUNS Number: 001912864
Project Start Date: 01-Jun-2011
Budget Start Date:
CFDA Code: 47.049
Project End Date: 31-May-2014
Budget End Date:
Agency: ?

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National Science Foundation
Project Funding Information for 2011:
Year Agency

Agency: The entity responsible for the administering of a research grant, project, or contract. This may represent a federal department, agency, or sub-agency (institute or center). Details on agencies in Federal RePORTER can be found in the FAQ page.

FY Total Cost
2011 NSF

National Science Foundation

$94,319

Results

i

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