S-Arithmetic Khintchine-Type Theorem

TL;DR

This paper proves a convergence Khintchine-type theorem in the S-arithmetic setting for products of non-degenerate v-adic manifolds, including the Archimedean case, extending classical Diophantine approximation results.

Contribution

It establishes a new convergence theorem in S-arithmetic Diophantine approximation for non-degenerate manifolds, incorporating the Archimedean place.

Findings

Proves a convergence Khintchine-type theorem in S-arithmetic setting

Extends classical results to product of v-adic manifolds including Archimedean case

Provides tools for Diophantine approximation on non-degenerate manifolds

Abstract

In this article we prove a convergence S-arithmetic Khintchine-type theorem for product of non-degenerate v-adic manifolds, where one of them is the Archimedian place.