Chris Hall

activity

20062026

most citedAn open image theorem for a general class of abelian varieties

49 citations · 127 across the 18 of their papers we have counts for

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15 papers · 1 filter

math.NT2026

Hasse-Weil Zeta Functions Modulo a Prime

Chris Hall

Let $F_{q}$ be a finite field of characteristic $p$ and $π : Y \to X$ be a finite $F_{q}$ -morphism of separated $F_{q}$ -schemes of finite type. Suppose $π$ …

math.NT2022

Class Field Theory and Arithmetic of Abelian Varieties over Local Fields

Christopher Stephen Hall

We use knowledge of local fields to adapt Jonathan Lubin and Michael Rosen's proof of Mazur's Proposition 4.39. This changes the result about abelian varieties from only working ov…

math.NT2018★ 3 cited

Variance of sums in arithmetic progressions of divisor functions associated with higher degree l-functions in $F_{q} (t)$

Chris Hall, Jonathan P. Keating, Edva Roditty-Gershon

We compute the variances of sums in arithmetic progressions of generalised k-divisor functions related to certain L-functions in $F_{q} (t)$ , in the limit as $q \to \infty$ . Th…

math.NT2017★ 3 cited

Variance of sums in arithmetic progressions of arithmetic functions associated with higher degree $L$ -functions in $F_{q} [t]$

Chris Hall, Jonathan P. Keating, Edva Roditty-Gershon

We compute the variances of sums in arithmetic progressions of arithmetic functions associated with certain $L$ -functions of degree two and higher in $F_{q} [t]$ , in the limi…

math.NT2015★ 2 cited

Explicit arithmetic of Jacobians of generalized Legendre curves over global function fields

Lisa Berger, Chris Hall, René Pannekoek +5

We study the Jacobian $J$ of the smooth projective curve $C$ of genus $r - 1$ with affine model $y^{r} = x^{r - 1} (x + 1) (x + t)$ over the function field $F_{p} (t)$ , when $p$ is p…

math.NT2014

Ramification of Compatible Systems on Curves and Independence of $ℓ$

Chris Hall

We show that certain ramification invariants associated to a compatible system of $ℓ$ -adic sheaves on a curve are independent of $ℓ$ .

Hasse-Weil Zeta Functions Modulo a Prime

Class Field Theory and Arithmetic of Abelian Varieties over Local Fields

Variance of sums in arithmetic progressions of divisor functions associated with higher degree l-functions in Fq​(t)

Variance of sums in arithmetic progressions of arithmetic functions associated with higher degree L-functions in Fq​[t]

Explicit arithmetic of Jacobians of generalized Legendre curves over global function fields

Ramification of Compatible Systems on Curves and Independence of ℓ

Variance of sums in arithmetic progressions of divisor functions associated with higher degree l-functions in $F_{q} (t)$

Variance of sums in arithmetic progressions of arithmetic functions associated with higher degree $L$ -functions in $F_{q} [t]$

Ramification of Compatible Systems on Curves and Independence of $ℓ$