Small value estimates for the multiplicative group

TL;DR

This paper extends Gel'fond's transcendence criterion to sequences of polynomials with small derivatives on large subsets of a subgroup of the complex multiplicative group, advancing transcendence theory techniques.

Contribution

It introduces a generalized criterion applicable to polynomial sequences with small derivatives on large subsets of multiplicative groups.

Findings

New transcendence criterion for polynomial sequences

Applicable to large subsets of complex multiplicative groups

Enhances methods in transcendence theory

Abstract

We generalize Gel'fond's transcendence criterion to the context of a sequence of polynomials whose first derivatives take small values on large subsets of a fixed subgroup of the multiplicative group C* of the field of complex numbers.