44 citations · 236 across the 15 of their papers we have counts for
9 papers · 2 filters
Average Frobenius distribution for elliptic curves defined over finite Galois extensions of the rationals
Kevin James, Ethan Smith
Let be a fixed number field, assumed to be Galois over . Let and be fixed integers with positive. Given an elliptic curve , defined over , we consi…
A Barban-Davenport-Halberstam asymptotic for number fields
Ethan Smith
Let be a fixed number field, and assume that is Galois over $\qq$. Previously, the author showed that when estimating the number of prime ideals with norm congruent to …
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…
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…
Group structures of elliptic curves over finite fields
Vorrapan Chandee, Chantal David, Dimitris Koukoulopoulos +1
It is well-known that if is an elliptic curve over the finite field , then for some pos…
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…