7 papers
Zeta functions of totally ramified p-covers of the projective line
Hanfeng Li, Hui June Zhu
In this paper we prove that there exists a Zariski dense open subset U defined over the rationals Q in the space of all one-variable rational functions with arbitrary k poles of pr…
L-functions of Exponential sums over one-dimensional affinoid: Newton over Hodge
Hui June Zhu
Let p be a prime and let F_pbar be the algebraic closure of the finite field of p elements. Let f(x) be any one variable rational function over F_pbar with n poles of orders d_1, .…
Asymptotic variation of L functions of one-variable exponential sums
Hui June Zhu
Let d>2 and let p be a prime coprime to d. Let Z_pbar be the ring of integers of Q_pbar. Suppose f(x) is a degree-d polynomial over Qbar and Z_pbar. Let P be a prime ideal over p i…
Families of supersingular curves in characteristic 2
Jasper Scholten, Hui June Zhu
This paper determines the normal forms of hyperelliptic supersingular curves of genus g over an algebraically closed field F of characteristic 2 for 0 < g< 9. We also show that eve…
Hyperelliptic curves in characteristic 2
Jasper Scholten, Hui June Zhu
In this paper we prove that there are no hyperelliptic supersingular curves over F_2bar of genus 2^n-1 for any integer n>1. Let g be a natural number, and h=floor(log_2(g+1)+1). Le…
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…