3 citations · 3 across the 3 of their papers we have counts for
5 papers
What is the height of two points in the plane?
Jesse Leo Kass, Frank Thorne
Here we describe the distribution of rational points on the Hilbert scheme of two points in the projective plane. More specifically, we explicitly describe a two-parameter family o…
Upper bounds on number fields of given degree and bounded discriminant
Robert J. Lemke Oliver, Frank Thorne
Let denote the number of degree number fields with discriminant bounded by . In this note, we improve the best known upper bounds on , finding that $N_n(X)…
Upper bounds on polynomials with small Galois group
Robert J. Lemke Oliver, Frank Thorne
When monic integral polynomials of degree are ordered by the maximum of the absolute value of their coefficients, the Hilbert irreducibility theorem implies that asympto…
Rank growth of elliptic curves in nonabelian extensions
Robert J. Lemke Oliver, Frank Thorne
Given an elliptic curve , it is a conjecture of Goldfeld that asymptotically half of its quadratic twists will have rank zero and half will have rank one. Nevertheles…
Levels of distribution for sieve problems in prehomogeneous vector spaces
Takashi Taniguchi, Frank Thorne
In a companion paper, we developed an efficient algebraic method for computing the Fourier transforms of certain functions defined on prehomogeneous vector spaces over finite field…