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arXiv · 2501.14839

A Note on the value distribution of some differential-difference monomials generated by a transcendental entire function of hyper-order less than one

Soumon Roy·Sudip Saha·Ritam Sinha
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Abstract

Let $\mathfrak{f}$ be a transcendental entire function with hyper-order less than one. The aim of this note is to study the value distribution of the differential-difference monomials $\alpha \mathfrak{f}(z)^{q_0}(\mathfrak{f}(z+c))^{q_1}$, where $c$ is a non-zero complex number and $q_0\geq2,$ $q_1\geq 1$ are non-negative integers, and $ \alpha(z)$ $(\not\equiv 0,\infty)$ be a small function of $\mathfrak{f}$.

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Soumon Roy, Sudip Saha, Ritam Sinha. 2025-01-24. A Note on the value distribution of some differential-difference monomials generated by a transcendental entire function of hyper-order less than one. https://arxiv.org/abs/2501.14839

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