62 citations · 134 across the 12 of their papers we have counts for
15 papers · 1 filter
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…
Three-isogeny Selmer groups and ranks of abelian varieties in quadratic twist families over a number field
Manjul Bhargava, Zev Klagsbrun, Robert J. Lemke Oliver +1
For an abelian variety over a number field , we prove that the average rank of the quadratic twists of is bounded, under the assumption that the multiplication-by-3 isog…
Unexpected biases in the distribution of consecutive primes
Robert J. Lemke Oliver, Kannan Soundararajan
While the sequence of primes is very well distributed in the reduced residue classes (mod ), the distribution of pairs of consecutive primes among the permissible pairs…
Effective log-free zero density estimates for automorphic -functions and the Sato-Tate conjecture
Robert J. Lemke Oliver, Jesse Thorner
Let be a number field. Let and be cuspidal automorphic representations of and , an…
Best possible densities of Dickson m-tuples, as a consequence of Zhang-Maynard-Tao
Andrew Granville, Daniel M. Kane, Dimitris Koukoulopoulos +1
We determine for what proportion of integers one now knows that there are infinitely many prime pairs as a consequence of the Zhang-Maynard-Tao theorem. We consider t…
The number of ramified primes in number fields of small degree
Robert J. Lemke Oliver, Frank Thorne
In this paper we investigate the distribution of the number of primes which ramify in number fields of degree d <= 5. In analogy with the classical Erdos-Kac theorem, we prove for…
The distribution of the Tamagawa ratio in the family of elliptic curves with a two-torsion point
Zev Klagsbrun, Robert J. Lemke Oliver
In recent work, Bhargava and Shankar have shown that the average size of the -Selmer group of an elliptic curve over is exactly , and Bhargava and Ho have shown…
Bounded gaps between primes in number fields and function fields
Abel Castillo, Chris Hall, Robert J. Lemke Oliver +2
The Hardy--Littlewood prime -tuples conjecture has long been thought to be completely unapproachable with current methods. While this sadly remains true, startling breakthroughs…
The distribution of 2-Selmer ranks of quadratic twists of elliptic curves with partial two-torsion
Zev Klagsbrun, Robert J. Lemke Oliver
This paper presents a new result concerning the distribution of 2-Selmer ranks in the quadratic twist family of an elliptic curve over an arbitrary number field K with a single poi…
Pretentiously detecting power cancellation
Junehyuk Jung, Robert J. Lemke Oliver
Granville and Soundararajan have recently introduced the notion of pretentiousness in the study of multiplicative functions of modulus bounded by 1, essentially the idea that two f…