$p$-adic Fourier theory for $\mathbf{Q}_{p^2}$ and the Monna map

TL;DR

This paper explores $p$-adic Fourier theory over the quadratic extension $ extbf{Q}_{p^2}$, revealing a novel valuation formula for the coefficients of relevant power series, which enhances understanding of $p$-adic harmonic analysis.

Contribution

It introduces a new valuation formula for power series coefficients in $p$-adic Fourier theory over $ extbf{Q}_{p^2}$, advancing the mathematical framework in this area.

Findings

Valuation formula for power series coefficients

Insights into $p$-adic Fourier analysis over quadratic extensions

Enhanced understanding of $p$-adic harmonic analysis

Abstract

We show that the coefficients of a power series occurring in $p$-adic Fourier theory for $\mathbf{Q}_{p^2}$ have valuations that are given by an intriguing formula.