Generalized Lindemann-Weierstrass and Gelfond-Schneider-Baker Theorems

TL;DR

This paper generalizes key theorems in transcendental number theory, introduces new transcendental numbers, and discusses their potential applications in cryptography and encryption.

Contribution

It extends classical theorems to identify new transcendental numbers and proposes their use in cryptographic methods.

Findings

New transcendental numbers identified

Methods for finding transcendental numbers developed

Potential cryptographic applications discussed

Abstract

We generalize Lindemann-Weierstrass theorem and Gelfond -Schneider-Baker Theorem. We find new transcendental numbers in this work. There are several methods to find transcendental numbers in the work. Recently transcendental numbers are applicable for cryptography (\cite{G}, \cite{K}, \cite{V}). Since we are able to make many tables of random numbers, the new transcendental numbers will be applicable for encryption and decryption in this work (\cite{V}, \cite{Z}).