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Authors
Affiliations
1 Department of Mathematics and Statistics, Queen’s University, Kingston, Ontario K7L 3N6, CA
2 School of Mathematics and Maxwell Institute for Mathematical Sciences, University of Edinburgh, Edinburgh, Scotland EH9 3JZ, GB
Source
Journal of the Ramanujan Mathematical Society, Vol 26, No 1 (2011), Pagination: 107-125
Abstract
In this paper, we investigate the properties of Ramanujan polynomials, a family of reciprocal polynomials with real coefficients originating from Ramanujan’s work. We begin by finding their number of real zeros, establishing a bound on their sizes, and determining their limiting values. Next, we prove that all nonreal zeros of Ramanujan polynomials lie on the unit circle, and are asymptotically uniformly distributed there. Finally, for each Ramunujan polynomial, we find all its zeros that are ischolar_mains of unity.