Zeros of Ramanujan-Like Polynomials

Abstract

In this paper we study a naturally occurring variant of Ramanujan polynomials with a Bernoulli convolution structure, $S_v$, related to the double Mordell-Tornheim series. In particular, we prove for even $v$ all zeros of $S_v$ lie on the complex unit circle, and for even $v\ge 4$ they are simple with the exception of roots at $1,-1$, which are double roots.