On the Zeros of Certain Entire Functions

2024/01/01 by Ruiming Zhang, Zhang, Ruiming
Mathematics · #Meromorphic and Entire Functions #Analytic Number Theory Research #Advanced Mathematical Identities

paper · pdf · doi:10.48550/arxiv.2401.01910

Abstract

In this work we prove that certain entire q-functions have infinitely many nonzero roots \ ρ_n\ _n=1^∞, as n→+∞ the moduli |ρ_n| 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 E_q(z,t).

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