On polynomials generated by the hyper-Fibonacci numbers.

Abstract

In this thesis, we construct sequences of polynomials whose coefficients are hyper-Fibonacci numbers and investigate certain properties of these polynomials. In particular, we obtain results about the number of their real zeros, behavior of their complex zeros as the degree increases, and Mahler measures of these polynomials with coefficients reduced modulo Lucas numbers. Most of our results are analogous to those concerning polynomials generated by the Fibonacci sequence, which appear in work of Garth, Mills, and Mitchell.

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