10 citations · 10 across the 1 of their papers we have counts for
7 papers
Improved bounds on number fields of small degree
Theresa C. Anderson, Ayla Gafni, Kevin Hughes +5
We study the number of degree number fields with discriminant bounded by . In this article, we improve an upper bound due to Schmidt on the number of such fields that was pr…
Quantitative Hilbert irreducibility and almost prime values of polynomial discriminants
Theresa C. Anderson, Ayla Gafni, Robert J. Lemke Oliver +3
We study two polynomial counting questions in arithmetic statistics via a combination of Fourier analytic and arithmetic methods. First, we obtain new quantitative forms of Hilbert…
An approximate form of Artin's holomorphy conjecture and non-vanishing of Artin -functions
Robert J. Lemke Oliver, Jesse Thorner, Asif Zaman
Let be a number field and be a finite group. Let be the family of number fields with absolute discriminant at most such that i…
Asymptotic identities for additive convolutions of sums of divisors
Robert J. Lemke Oliver, Sunrose T. Shrestha, Frank Thorne
In a 1916 paper, Ramanujan studied the additive convolution of sum-of-divisors functions and , and proved an asymptotic formula for it when and $…
Improved lower bounds for the number of fields with alternating Galois group
Aaron Landesman, Robert J. Lemke Oliver, Frank Thorne
Let be an integer. We prove that the number of number fields with Galois group and absolute discriminant at most is asymptotically at least .…
Elements of given order in Tate-Shafarevich groups of abelian varieties in quadratic twist families
Manjul Bhargava, Zev Klagsbrun, Robert J. Lemke Oliver +1
Let be an abelian variety over a number field and let be a prime. Cohen-Lenstra-Delaunay-style heuristics predict that the Tate-Shafarevich group of should contai…