Olivia 042.jpg

Olivia Beckwith

Number theorist

Welcome to my personal webpage. 

On this site, you can read short introductions to some areas I'm interested in and find links to most of my papers and preprints.  

The math images were made using Mathematica. 

Research Interests

Research Interests

Number theory began with elementary questions about the numbers we count with. It has grown from simple and tangible questions about integers into an impressive range of abstract subdisciplines spanning geometry, analysis, and algebra, with practical applications in cryptography. 

My research interests touch on algebraic number theory, combinatorial number theory, and analytic number theory. To be more specific, I study modular forms, which are analytic functions that encode a wide variety of arithmetic information in various ways and play a central role in modern number theory. My work explores connections between elliptic modular forms and quadratic number fields, integer partitions, and L-functions and endeavors to push our understanding of them a little further. 

 

Recent Publications

Scarcity of congruences for the partition function (with Scott Ahlgren and Martin Raum). Submitted. Link. 

Non-holomorphic Ramanujan-type congruences for Hurwitz class numbers (with Martin Raum and Olav Richter). Proc. Natl. Acad. Sci. USA (PNAS), 117 (2020), no. 36, 21953-21961. Link.

A zero density estimate and fractional imaginary parts of zeros for GL(2) L-functions (with D. Liu, J. Thorner, and A. Zaharescu). Submitted. Link.

Contact
Information

Department of Mathematics

411 Gibson Hall

Tulane University

New Orleans