This paper demonstrates that zeros of reciprocal polynomials lie on the unit circle, implying a key result for Ramanujan polynomials.
We settle a conjecture proposed by B. Maji and T. Sarkar regarding the location of zeros of a two-parameter family of reciprocal polynomials, Rk,(z) for positive integers k and . These polynomials are generalizations of Ramanujan polynomials studied by M. R. Murty, C. Smyth, and R. Wang. More specifically, we show that except for two real zeros, all other zeros of Rk,(z) lie on the unit circle.
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Charan et al. (2025) studied this question.
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