On a conjecture of Heim and Neuhauser on some polynomials arising frommodular forms and related to Fibonacci polynomials
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Date
2022
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Université de M'sila
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. We prove this conjecture, and deduce some identities for Fibonacci
numbers and determine the modes of another sequence related to Fibonacci polynomials.
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Keywords
Fibonacci number · Log–concave sequence · Polynomial · Zeros