References & Citations
Mathematics > Complex Variables
Title: On the Zeros of Certain Entire Functions
(Submitted on 1 Jan 2024 (v1), last revised 30 Jan 2024 (this version, v4))
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 $\mathcal{E}_{q}(z,t)$.
Submission history
From: R Zhang Dr. [view email][v1] Mon, 1 Jan 2024 11:48:49 GMT (7kb)
[v2] Sun, 7 Jan 2024 07:49:26 GMT (7kb)
[v3] Thu, 18 Jan 2024 13:03:30 GMT (7kb)
[v4] Tue, 30 Jan 2024 08:46:03 GMT (8kb)
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