64 citations · 140 across the 23 of their papers we have counts for
4 papers · 1 filter
On the existence of large degree Galois representations for fields of small discriminant
Jeremy Rouse, Frank Thorne
Let be a Galois extension of number fields. We prove two lower bounds on the maximum of the degrees of the irreducible complex representations of , the sharpe…
An error estimate for counting -sextic number fields
Takashi Taniguchi, Frank Thorne
In this note, we prove a power-saving remainder term for the function counting -sextic number fields. We also give a prediction on the second main term. We also present numeri…
Four Perspectives on Secondary Terms in the Davenport-Heilbronn Theorems
Frank Thorne
This paper is an expanded version of the author's lecture at the Integers Conference 2011. We discuss the secondary terms in the Davenport-Heilbronn theorems on cubic fields and 3-…
Bubbles of congruent primes
Frank Thorne
Shiu proved that if a and q are arbitrary coprime integers, then there exist arbitrarily long strings of consecutive primes which are all congruent to a modulo q. We generalize Shi…