3 citations · 3 across the 2 of their papers we have counts for
4 papers
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…
The Generalized Nagell-Ljunggren Problem: Powers with Repetitive Representations
Andrew Bridy, Robert J. Lemke Oliver, Arlo Shallit +1
We consider a natural generalization of the Nagell-Ljunggren equation to the case where the qth power of an integer y, for q >= 2, has a base-b representation that consists of a le…