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Minimize RSR Award Detail

Research Spending & Results

Award Detail

Awardee:UNIVERSITY OF GEORGIA RESEARCH FOUNDATION, INC.
Doing Business As Name:University of Georgia Research Foundation Inc
PD/PI:
  • Paul Pollack
  • (706) 542-5939
  • pollack@uga.edu
Award Date:07/11/2020
Estimated Total Award Amount: $ 168,000
Funds Obligated to Date: $ 168,000
  • FY 2020=$168,000
Start Date:07/15/2020
End Date:06/30/2023
Transaction Type:Grant
Agency:NSF
Awarding Agency Code:4900
Funding Agency Code:4900
CFDA Number:47.049
Primary Program Source:040100 NSF RESEARCH & RELATED ACTIVIT
Award Title or Description:Statistical Questions in Number Theory and Arithmetic Geometry
Federal Award ID Number:2001581
DUNS ID:004315578
Program:ALGEBRA,NUMBER THEORY,AND COM
Program Officer:
  • Andrew Pollington
  • (703) 292-4878
  • adpollin@nsf.gov

Awardee Location

Street:310 East Campus Rd
City:ATHENS
State:GA
ZIP:30602-1589
County:Athens
Country:US
Awardee Cong. District:10

Primary Place of Performance

Organization Name:University of Georgia
Street:310 East Campus Rd.
City:Athens
State:GA
ZIP:30602-1589
County:Athens
Country:US
Cong. District:10

Abstract at Time of Award

Number theory is a thriving area of mathematics research with deep connections to both computer science and digital security. The principal goal of this project is to deepen our understanding of certain ubiquitous number-theoretic objects (such as elliptic curves, power residues modulo prime numbers, and classical arithmetic functions such as Euler's phi-function), by studying them through a quantitative lens. One novel feature of this work is an approach to these problems that takes advantage of our understanding of the "anatomy of integers" describing the typical way a number breaks down into component parts (prime factors). Three main topics of investigation will be pursued: (1) A detailed study of the value-distribution of arithmetic functions, one particular problem being to pin down precise conditions under which a number has many factorizations. Here "factorizations" may be ordered or unordered, and we may wish to impose certain additional conditions on the parts. (2) The distribution of power residues. (3) The statistical distribution of torsion structures of elliptic curves. For (1) and (3), results from the "anatomy integers" will play a critical role. For (2), the PI plans to supplement the existing approaches to such problems - which have been mostly analytic, involving character sums - with algebraic approaches that make use of higher reciprocity laws. This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.

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