Skip Navigation Links

Project Information

CRITICAL ZEROS OF L-FUNCTIONS

Agency:
NSF

National Science Foundation

Project Number:
1406981
Contact PI / Project Leader:
IWANIEC, HENRYK
Awardee Organization:
RUTGERS THE ST UNIV OF NJ NEW BRUNSWICK

Description

Abstract Text:
This project concerns research in the Theory of Numbers, in particular questions related to the distribution of prime numbers. This topic has advanced considerably during the past year due to the breakthrough work of Zhang and Maynard on small gaps between consecutive prime numbers, where previous work of Fouvry, Iwaniec, and Friedlander played a crucial role. One of the most fundamental open questions in modern mathematics is the Riemann hypothesis, which connects the distribution of prime numbers with the distribution of complex zeros of the generating zeta function. The hypothesis asserts that all these zeros lie on a single "critical" line. The main goal of this project is to show that a large proportion of these zeros are indeed resting there. This result will enhance our understanding of subtle behavior of the basic elements of arithmetic, the prime numbers. The PI has written expository books on several topics related to the Theory of Numbers, most recently a book on Sieve Methods, joint with John Friedlander. The PI is active in training graduate students and plans to continue to train graduate students under this award.

The project starts with the method of Levinson-Conrey designed for estimating the percentage of zeros of the Riemann zeta function that are on the critical line. The original construction by Conrey of a linear combination of the zeta function and its odd order derivatives is quite robust. Naturally, this needs to be mollified by a suitable Dirichlet polynomial. The longer mollifier one can handle, the more critical zeros reveal. The key innovation of the proposed approach is a special arrangement of the convolution coefficients into "local mollifiers" which allows applying very long global mollification, thus raising hope for substantial improvements of the existing results.
Project Terms:
Arithmetic; Award; Behavior; Books; Complex; design; Elements; Goals; graduate student; innovation; Joints; Mathematics; Methods; Play; Research; Rest; Role; theories; Training; Work; Writing

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: 2014
Award Notice Date: 18-Jun-2014
DUNS Number: 001912864
Project Start Date: 01-Jul-2014
Budget Start Date:
CFDA Code: 47.049
Project End Date: 30-Jun-2017
Budget End Date:
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.

National Science Foundation
Project Funding Information for 2014:
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
2014 NSF

National Science Foundation

$97,435

Results

i

It is important to recognize, and consider in any interpretation of Federal RePORTER data, that the publication and patent information cannot be associated with any particular year of a research project. The lag between research being conducted and the availability of its results in a publication or patent award varies substantially. For that reason, it's difficult, if not impossible, to associate a publication or patent with any specific year of the project. Likewise, it is not possible to associate a publication or patent with any particular supplement to a research project or a particular subproject of a multi-project grant.

ABOUT FEDERAL REPORTER RESULTS

Publications: i

Click on the column header to sort the results

PubMed = PubMed PubMed Central = PubMed Central Google Scholar = Google Scholar

Patents: i

Click on the column header to sort the results

Similar Projects

Download Adobe Acrobat Reader:Adobe Acrobat VERSION: 3.41.0 Release Notes
Back to Top