Zeros and convergent subsequences of Stern polynomials

We investigate Dilcher and Stolarsky’s polynomial analogue of the Stern diatomic sequence. Basic information is obtained concerning the distribution of their zeros in the plane. Also, uncountably many subsequences are found, each of which converges to a unique analytic function on the open unit disk. We thus generalize a result of Dilcher and Stolarsky from their second paper on the subject.