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math.NT1998
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…
math.NT1998
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…
math.NT1998
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…