Variant of Ramanujan polynomials and a conjecture of Maji & Sarkar

We settle a conjecture proposed by B. Maji and T. Sarkar [ Zeros of Ramanujan-type polynomials , arXiv:2306.10283] regarding the location of zeros of a two-parameter family of reciprocal polynomials, R k , ℓ ( z ) Rk,(z) for positive integers k k and ℓ . These polynomials are generalizations of Ramanujan polynomials studied by M. R. Murty, C. Smyth, and R. Wang [J. Ramanujan Math. Soc. 26 (2011), pp. 107–125]. More specifically, we show that except for two real zeros, all other zeros of R k , ℓ ( z ) Rk,(z) lie on the unit circle.