Olivia Beckwith

Hello and welcome to my page! I am a mathematician currently working as a J. Doob Assistant Professor at the University of Illinois at Urbana-Champaign.

I'm a number theorist and I specialize in modular forms, which are analytic functions that encode arithmetic information in various ways. I'm particularly interested in applications of the theory of elliptic modular forms to the study of quadratic number fields and integer partitions.

You can contact me by emailing me at obeck@illinois.edu .

My cv is here.

Publications and preprints

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

12. 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.

11. Class number divisibility for imaginary quadratic fields. Research in Number Theory, Res. Number Theory 6 (2020), no. 1, Paper No. 13. Link.

10. Indivisibility of class numbers of imaginary quadratic fields. Res. Math. Sci. 4 20 (2017). Link.

9. Extracting aggregation free energies of mixed clusters from simulations of small systems (with James Kindt, Lara Patel, Robert Schneider, Xiaokun Zhang). J. Chem. Theor. Comp. 13, p. 5195-5206 (2017). Link.

8. Bounds for special values of shifted convolution Dirichlet series. Proc. Amer. Math. Soc. 145 6 (2017). p. 2373-2381. Link.

7. On the number of parts of integer partitions lying in given residue classes (with Michael Mertens). Annals of Combinatorics 21 (2017), p. 507-517. Link.

6. The number of parts in certain residue classes of integer partitions (with Michael Mertens). Research in Number Theory 1 (2015). Link.

5. Multiplicative Properties of the Number of k-Regular Partitions (with Christine Bessenrodt). Annals of Combinatorics 20 (2016), p. 231-250. Link.

4. Distribution of eigenvalues of weighted, structured matrix ensembles (with Victor Luo, Steven J. Miller, Karen Shen, Nicholas Triantafillou), Integers: Electronic Journal of Combinatorial Number Theory 15 (2015). Link.

3. Generalized Ramanujan Primes (with Nadine Amersi, Steven J. Miller, Ryan Ronan, Jonathan Sondow), Combinatorial and Additive Number Theory, CANT 2011 and 2012, Springer Proceedings in Mathematics and Statistics (2014), 1-13. Link.

2. The Average Gap Distribution for Generalized Zeckendorf Decompositions (with Amanda Bower, Louis Gaudet, Rachel Insoft, Shiyu Li, Steven J. Miller, Philip Tosteson). The Fibonacci Quarterly ( 51 (2013), 13--27). Link.

1. Minkowski length of 3D lattice polytopes (with Matt Grimm, Jenya Soprunova, Bradley Weaver). Journal of Discrete and Computational Geometry. (48, Issue 4 (2012), 1137-1158). Link.