M. Schmidt

activity

20172023

collaborators

5 papers

math.NT2023

On a Fiber Conjecture of Wan

Matthew Schmidt

For a prime $p$ and $p$ -power $q$ , let $f (x) \in F_{q} [x]$ with $deg f$ coprime to $p$ . As $λ$ varies in $F_{p}^{\times}$ , Wan has conjectured that t…

math.NT2021

A determinant of the Artin-Hasse exponential coefficients

Matthew Schmidt

We present a new determinant identity involving the coefficients of the Artin-Hasse exponential. In particular, if $E(x) = \exp(\sum_{k=0}^\infty \frac{x^{p^k}}{p^k}) = \sum_{n=0}^…

math.NT2019

Exponential Sums of Witt Towers over Affinoids

Matthew Schmidt

In this paper we construct a Dwork theory for general exponential sums over affinoids in Witt towers. Using this, we compute the degree of the $L$ -function, its Hodge polygon and e…

math.NT2019

$T$ -adic Exponential Sums over Affinoids

Matthew Schmidt

We introduce and develop $(π, p)$ -adic Dwork theory for $L$ -functions of exponential sums associated to one-variable rational functions, interpolating $p^{k}$ -order exponential sums o…

math.NT2017

Schmid's Formula for Higher Local Fields

Matthew Schmidt

In local class field theory, the Schmid-Witt symbol encodes interesting data about the ramification theory of $p$ -extensi-ons of $K$ and can, for example, be used to compute the hi…

On a Fiber Conjecture of Wan

A determinant of the Artin-Hasse exponential coefficients

Exponential Sums of Witt Towers over Affinoids

T-adic Exponential Sums over Affinoids

Schmid's Formula for Higher Local Fields

$T$ -adic Exponential Sums over Affinoids