Chourasiya–Jamal–Maji–Sarkar conjecture on zeros of Ramanujan-type polynomials

Let $k\in\mathbb{N}$ and let $p$ be a prime number. Define the Ramanujan-type polynomial

$$R_{2k+1,p}(z):=\sum_{j=1}^k(p^{2j}-1)(p^{2k+2-2j}-1)\frac{B_{2j}B_{2k+2-2j}}{(2j)!(2k+2-2j)!}(pz)^{2k+2-2j}.$$

Conjecture on the zeros of $R_{2k+1,p}$. The only real root of $R_{2k+1,p}(z)$ is $z=0$, with multiplicity $2$; moreover, its non-real roots are simple and lie on the circle $|z|=1/p$. This conjecture concerns the zero distribution of a Ramanujan-type polynomial arising from a Grosswald-type formula for a Dirichlet $L$-function. It extends the known unit-circle result for the non-real roots of the classical Ramanujan polynomials, but the supplied text gives no resolution of the conjecture.