Abstract
Let
where \(\alpha >0,~0<q<1.\) In a paper of Ruiming Zhang, he asked under what conditions the zeros of the entire function \(A_{q}^{(\alpha )}(a;z)\) are all real and established some results on the zeros of \(A_{q}^{(\alpha )}(a;z)\) which present a partial answer to that question. In the present paper, we will set up some results on certain entire functions which includes that \(A_{q}^{(\alpha )}(q^l;z),~l\ge 2\) has only infinitely many negative zeros that gives a partial answer to Zhang’s question. In addition, we establish some results on zeros of certain entire functions involving the Rogers–Szegő polynomials and the Stieltjes–Wigert polynomials.
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Acknowledgements
This work was partially supported by the National Natural Science Foundation of China (Grant No. 11801451).
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He, B. On Zeros of Some Entire Functions. Results Math 74, 52 (2019). https://doi.org/10.1007/s00025-019-0978-y
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DOI: https://doi.org/10.1007/s00025-019-0978-y
Keywords
- zeros of entire functions
- Pólya frequence sequence
- Vitali’s theorem
- Hurwitz’s theorem
- Rogers–Szegő polynomials
- Stieltjes–Wigert polynomials