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arXiv · 2401.01910

On the Zeros of Certain Entire Functions

Ruiming Zhang
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Abstract

In this work we prove that certain entire $q$-functions have infinitely many nonzero roots $\left\{ \rho_{n}\right\} _{n=1}^{\infty}$, as $n\to+\infty$ the moduli $\left|\rho_{n}\right|$ grow at least exponentially. Applications to entire $q$-functions defined by series expansions are provided. These functions include the $q$-analogue of the plane wave function $\mathcal{E}_{q}(z,t)$.

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Ruiming Zhang. 2024-01-01. On the Zeros of Certain Entire Functions. https://arxiv.org/abs/2401.01910

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