18 citations · 39 across the 3 of their papers we have counts for
3 papers
math.NT2012★ 7 cited
A generalization of the Barban-Davenport-Halberstam Theorem to number fields
Ethan Smith
For a fixed number field , we consider the mean square error in estimating the number of primes with norm congruent to modulo by the Chebotarëv Density Theorem when aver…
math.NT2012★ 14 cited
Finite field elements of high order arising from modular curves
Jessica F. Burkhart, Neil J. Calkin, Shuhong Gao +6
In this paper, we recursively construct explicit elements of provably high order in finite fields. We do this using the recursive formulas developed by Elkies to describe explicit…
math.NT2012★ 18 cited
Elliptic curves, modular forms, and sums of Hurwitz class numbers
Brittany Brown, Neil J. Calkin, Timothy B. Flowers +3
Let H(N) denote the Hurwitz class number. It is known that if is a prime, then {equation*} \sum_{|r|<2\sqrt p}H(4p-r^2) = 2p. {equation*} In this paper, we investigate the beha…