On a conjecture of Heim and Neuhauser on some polynomials arising frommodular forms and related to Fibonacci polynomials

Yahia ZouaregMoussa Benoumhani2022-09-122022-09-122022http://dspace.univ-msila.dz:8080//xmlui/handle/123456789/31475Heim 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.Fibonacci number · Log–concave sequence · Polynomial · ZerosOn a conjecture of Heim and Neuhauser on some polynomials arising frommodular forms and related to Fibonacci polynomialsArticle