14 citations · 14 across the 1 of their papers we have counts for
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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…
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…
Large torsion subgroups of split Jacobians of curves of genus two or three
Everett W. Howe, Franck Leprevost, Bjorn Poonen
We construct examples of families of curves of genus 2 or 3 over Q whose Jacobians split completely and have various large rational torsion subgroups. For example, the rational poi…
Real polynomials with all roots on the unit circle and abelian varieties over finite fields
Stephen A. DiPippo, Everett W. Howe
In this paper we prove several theorems about abelian varieties over finite fields by studying the set of monic real polynomials of degree 2n all of whose roots lie on the unit cir…