Abstract:
Heim and Neuhauser investigated some polynomials related to the Dedekind function.
They proved the log-concavity of these polynomials and conjectured that they have only
real zeros. In this thesis, we prove this conjecture, and deduce some identities for Fibonacci
numbers and determine the modes of another sequence related to Fibonacci polynomials. We
have also studied solution of some diophantine equations.
