Joe Kramer-Miller

activity

20162025

most cited

p

-adic estimates of exponential sums on curves

7 citations · 16 across the 12 of their papers we have counts for

collaborators

13 papers

math.NT2025

Ekedahl-Oort types of $Z /2 Z$ -covers in characteristic $2$

Jeremy Booher, Steven R. Groen, Joe Kramer-Miller

In this article we study the Ekedahl-Oort types of $Z /2 Z$ -Galois covers $π : Y \to X$ in characteristic two. When the base curve $X$ is ordinary, we show that the E…

math.CO2025

The diagonal and Hadamard grade of hypergeometric functions

Andrew Harder, Joe Kramer-Miller

Diagonals of rational functions are an important class of functions arising in number theory, algebraic geometry, combinatorics, and physics. In this paper we study the diagonal gr…

math.NT2024

Iwasawa theory of Frobenius-torsion class group schemes

Jeremy Booher, Bryden Cais, Joe Kramer-Miller +1

We establish a new Iwasawa theory for the kernel of Frobenius on Jacobians of curves in geometric $Z_{p}$ -towers over the projective line in characteristic $p$ , thereby prov…

math.NT2024

Transcendence properties of the Artin-Hasse exponential modulo $p$

Joe Kramer-Miller

Let $E_{p} (x)$ denote the Artin-Hasse exponential and let $E_{p} (x)$ denote its reduction modulo $p$ in $F_{p} [[x]]$ . In this article we study transcendence propertie…

math.NT2023

Zeros of the Goss zeta function

Joe Kramer-Miller, James Upton

Let $X$ be a smooth proper curve over a finite field and let $\infty \in X$ be a closed point. Let $A$ be the ring of functions on $X - \infty$ . The Goss zeta function $ζ_{A}$ of $A$ …

math.NT2021

Newton Polygons of Sums on Curves II: Variation in $p$ -adic Families

Joe Kramer-Miller, James Upton

In this article we study the behavior of Newton polygons along $Z_{p}$ -towers of curves. Fix an ordinary curve $X$ over a finite field $F_{q}$ of characteristic $p$ .…

math.NT2021★ 1 cited

Newton Polygons of Sums on Curves I: Local-to-Global Theorems

Joe Kramer-Miller, James Upton

The purpose of this article is to study Newton polygons of certain abelian $L$ -functions on curves. Let $X$ be a smooth affine curve over a finite field $F_{q}$ and let $ρ:π…

math.NT2020

Some unlikely intersections between the Torelli locus and Newton strata in $A_{g}$

Joe Kramer-Miller

Let $p$ be an odd prime. What are the possible Newton polygons for a curve in characteristic $p$ ? Equivalently, which Newton strata intersect the Torelli locus in $A_{g}$ ?…

math.NT2020

$p$ -adic estimates of abelian Artin $L$ -functions on curves

Joe Kramer-Miller

The purpose of this article is to prove a "Newton over Hodge" result for finite characters on curves. Let $X$ be a smooth proper curve over a finite field $F_{q}$ of charact…

math.NT2019★ 7 cited

$p$ -adic estimates of exponential sums on curves

Joe Kramer-Miller

The purpose of this article is to prove a ``Newton over Hodge'' result for exponential sums on curves. Let $X$ be a smooth proper curve over a finite field $F_{q}$ of charac…

math.NT2019★ 2 cited

Log-decay $F$ -isocrystals on higher dimensional varieties

Joe Kramer-Miller

Let $k$ be a perfect field of positive characteristic and let $X$ be a smooth irreducible quasi-compact scheme over $k$ . The Drinfeld-Kedlaya theorem states that for an irreducible…

math.NT2018

The monodromy of unit-root $F$ -isocrystals with geometric origin

Joe Kramer-Miller

Let $C$ be a smooth curve over a finite field in characteristic $p$ and let $M$ be an overconvergent $F$ -isocrystal over $C$ . After replacing $C$ with a dense open subset $M$ obtai…

math.NT2016★ 6 cited

The monodromy of $F$ -isocrystals with log-decay

Joe Kramer-Miller

Let U be a smooth geometrically connected affine curve over $F_{p}$ with compactification X. Following Dwork and Katz, a $p$ -adic representation $ρ$ of $π_{1} (U)$ corresponds…

Ekedahl-Oort types of Z/2Z-covers in characteristic 2

The diagonal and Hadamard grade of hypergeometric functions

Iwasawa theory of Frobenius-torsion class group schemes

Transcendence properties of the Artin-Hasse exponential modulo p

Zeros of the Goss zeta function

Newton Polygons of Sums on Curves II: Variation in p-adic Families

Newton Polygons of Sums on Curves I: Local-to-Global Theorems

Some unlikely intersections between the Torelli locus and Newton strata in Ag​

p-adic estimates of abelian Artin L-functions on curves

p-adic estimates of exponential sums on curves

Log-decay F-isocrystals on higher dimensional varieties

The monodromy of unit-root F-isocrystals with geometric origin

The monodromy of F-isocrystals with log-decay

Ekedahl-Oort types of $Z /2 Z$ -covers in characteristic $2$

Transcendence properties of the Artin-Hasse exponential modulo $p$

Newton Polygons of Sums on Curves II: Variation in $p$ -adic Families

Some unlikely intersections between the Torelli locus and Newton strata in $A_{g}$

$p$ -adic estimates of abelian Artin $L$ -functions on curves

$p$ -adic estimates of exponential sums on curves

Log-decay $F$ -isocrystals on higher dimensional varieties

The monodromy of unit-root $F$ -isocrystals with geometric origin

The monodromy of $F$ -isocrystals with log-decay