$p$-Adic $\lambda$ Functions for Cyclic Mumford Curve

TL;DR

This paper introduces a new way to express branch points of cyclic Mumford curves using $p$-adic theta functions evaluated at the p-adic period matrix, linking algebraic geometry with p-adic analysis.

Contribution

It provides a novel expression for branch points cross ratios of cyclic Mumford curves in terms of $p$-adic theta functions.

Findings

Expressed branch points cross ratio as quotients of $p$-adic theta functions

Connected algebraic properties of Mumford curves with p-adic analysis

Established a new framework for studying cyclic Mumford curves

Abstract

We express the branch points cross ratio of cyclic Mumford curves as quotients of $p$-adic theta functions evaluated at the p-adic period matrix