Patrick Erik Bradley

activity

20242026

collaborators

6 papers

math.NT2026

Hearing Tamagawa Factors modulo $q - 1$

Patrick Erik Bradley

The Tamagawa factor w.r.t.\ the prime $p$ of an abelian variety $A$ over a non- archimedean local field $K$ is found to be congruent modulo $q - 1$ to the wavelet eigenvalues of a…

math.PR2026

$p$ -Adic Diffusion and Random Walks on $[0, 1]$

Patrick Erik Bradley, Paulina Halwas, Ell Ari Nitsche +2

Integral operators on the real unit interval are constructed as transported from ones on the $p$ -adic unit disc via the Monna map. This gives rise to strong Markov processes on $[0…

math.NT2026

Boundary Value Problems on $p$ -Adic Analytic Manifolds

Patrick Erik Bradley

An account is given on newest developments on $p$ -adic boundary value problems on $p$ -adic analytic manifolds and their relationship with diffusion. In particular, novel coordinate…

math.NT2025

Hearing the Serre invariant of a compact $p$ -adic analytic manifold

Patrick Erik Bradley, Ãngel MorÃ¡n Ledezma

Using a previous novel way of defining kernel functions for Laplacian integral operators on a compact $p$ -adic analytic manifold $X$ , one such operator $I^_{0}^{s}$ with $s\in\mathds{R…

math.AP2025

Boundary Value Problems for p-Adic Elliptic Parisi-ZÃºÃ±iga Diffusion

Patrick Erik Bradley

Elliptic integral-differential operators resembling the classical elliptic partial differential equations are defined over a compact d-dimensional p-adic domain together with assoc…

math.NT2024

Schottky invariant diffusion on the transcendent p-adic upper half plane

Patrick Erik Bradley

The transcendent part of the Drinfeld p-adic upper half plane is shown to be a Polish space. Using Radon measures associated with regular differential 1-forms invariant under Schot…

Hearing Tamagawa Factors modulo q−1

p-Adic Diffusion and Random Walks on [0,1]

Boundary Value Problems on p-Adic Analytic Manifolds

Hearing the Serre invariant of a compact p-adic analytic manifold

Boundary Value Problems for p-Adic Elliptic Parisi-ZÃºÃ±iga Diffusion

Schottky invariant diffusion on the transcendent p-adic upper half plane

Hearing Tamagawa Factors modulo $q - 1$

$p$ -Adic Diffusion and Random Walks on $[0, 1]$

Boundary Value Problems on $p$ -Adic Analytic Manifolds

Hearing the Serre invariant of a compact $p$ -adic analytic manifold