A Schanuel property for exponentially transcendental powers

TL;DR

This paper establishes a Schanuel-type property for exponentially transcendental powers, extending classical conjectures to real and complex numbers, with implications for transcendence theory.

Contribution

It proves an analogue of Schanuel's conjecture for exponentially transcendental real powers and generalizes the result to multiple powers in complex settings.

Findings

Most real numbers are exponentially transcendental.

The paper extends Schanuel's conjecture to exponential transcendence.

Results encompass both real and complex cases.

Abstract

We prove the analogue of Schanuel's conjecture for raising to the power of an exponentially transcendental real number. All but countably many real numbers are exponentially transcendental. We also give a more general result for several powers in a context which encompasses the complex case.