On Zeros of Some Entire Functions

Let $$\begin{aligned} A_{q}^{(\alpha )}(a;z)=\sum _{k=0}^{\infty }\frac{(a;q)_{k}q^{\alpha k^2} z^k}{(q;q)_{k}}, \end{aligned}$$Aq(α)(a;z)=∑k=0∞(a;q)kqαk2zk(q;q)k,where $$\alpha >0,~0<q<1.$$α>0,0<q<1. In a paper of Ruiming Zhang, he asked under what conditions the zeros of the entire function $$A_{q}^{(\alpha )}(a;z)$$Aq(α)(a;z) are all real and established some results on the zeros of $$A_{q}^{(\alpha )}(a;z)$$Aq(α)(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 $$A_{q}^{(\alpha )}(q^l;z),~l\ge 2$$Aq(α)(ql;z),l≥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.