Transcendence of certain sequences of algebraic numbers

TL;DR

This paper employs Schmidt's Subspace Theorem to enhance and generalize transcendence results for sequences of algebraic numbers, connecting to Erdős's work on the irrationality of sequences.

Contribution

It introduces new transcendence theorems for algebraic number sequences, extending previous results using advanced Diophantine approximation techniques.

Findings

Improved transcendence criteria for algebraic sequences

Extended theorems related to Erdős's irrationality results

Connections established between Schmidt's theorem and sequence transcendence

Abstract

Using Schmidt's Subspace Theorem, this paper improves and extends an existing transcendence result for sequences of algebraic numbers. The theorems thus produced correspond to a central theorem on the irrationality of sequences due to Erd\H{o}s.