Profile for Kelly O'Connor

Kelly O'Connor, Mathematics & Statistics, co-authored the article "Unit lattices of D4-quartic number fields with signature (2,1)" in "Journal of Number Theory," Volume 280, March 2026 published on March 15 by Elsevier. In joint work with Sara Chari, St. Mary’s College of Maryland; Sergio Ricardo Zapata Ceballos, Youngstown State University; Erik Holmes, University of Toronto; Fatemeh Jalalvand, University of Calgary; Rahinatou Yuh Njah Nchiwo, Aalto University; Fabian Ramirez, University of California Irvine; and Sameera Vemulapalli, Harvard University; we investigate the set of unit shapes for D4-quartic number fields with two real embeddings and one pair of complex conjugate embeddings. We show this set consists entirely of transcendental elements and prove that its set of limits points contains at least three explicit algebraic numbers.

Submitted on: July 2

Kelly O'Connor, Mathematics & Statistics, co-authored the article "Nonsplitting of the Hilbert exact sequence and the principal Chebotarev density theorem" in "The Ramanujan Journal Volume 68," article number 125 (2025), published on Dec. 12, 2025, by Springer. In joint work with Lian Duan, ShanghaiTech University; Ning Ma, State University of New York at Buffalo; and Xiyuan Wang, The Ohio State University. Given K/k a finite Galois extension of number fields, we find a way of verifying the non-splitting of the Hilbert short exact sequence by finite calculation. Our method is based on the study of the principal version of the Chebotarev density theorem, which represents the density of the prime ideals of k that factor into the product of principal prime ideals in K. We also find explicit equations to express the principal density in terms of the invariants of K/k. In particular, we prove that the group structure of the ideal class group of K can be determined by reading the principal densities.

Submitted on: July 2