14 citations · 14 across the 1 of their papers we have counts for
9 papers
Curves of every genus with many points, II: Asymptotically good families
Noam D. Elkies, Everett W. Howe, Andrew Kresch +3
We resolve a 1983 question of Serre by constructing curves with many points of every genus over every finite field. More precisely, we show that for every prime power q there is a…
On the nonexistence of certain curves of genus two
Everett W. Howe
We prove that if q is a power of an odd prime then there is no genus-2 curve over F_q whose Jacobian has characteristic polynomial of Frobenius equal to x^4 + (2-2q)x^2 + q^2. Our…
Appendix to a paper of Maisner and Nart
Everett W. Howe
We prove that there is no genus-2 curve over F_q whose Jacobian has characteristic polynomial of Frobenius equal to x^4 + (1 - 2q) x^2 + q^2. Maisner and Nart had observed (by dire…
On the group orders of elliptic curves over finite fields
Everett W. Howe
Given a prime power q, for every pair of positive integers m and n with m dividing the GCD of n and q-1, we construct a modular curve over F_q that parametrizes elliptic curves ove…
On the existence of absolutely simple abelian varieties of a given dimension over an arbitrary field
Everett W. Howe, Hui June Zhu
We prove that for every field k and every positive integer n, there exists an absolutely simple n-dimensional abelian variety over k. We also prove an asymptotic result for finite…
Higher-order Carmichael numbers
Everett W. Howe
We define a Carmichael number of order m to be a composite integer n such that nth-power raising defines an endomorphism of every Z/nZ-algebra that can be generated as a Z/nZ-modul…