Recurrence relations for polynomials obtained by arithmetic functions

DOI10.1142/S1793042119500726zbMath1435.11055OpenAlexW2911983332WikidataQ128512221 ScholiaQ128512221MaRDI QIDQ5223036

Markus Neuhauser, Bernhard E. Heim, Florian Luca

Publication date: 4 July 2019

Published in: International Journal of Number Theory (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1142/s1793042119500726

zbMATH Keywords

polynomialsrecurrence relationDedekind eta functionarithmetic functions

Mathematics Subject Classification ID

Combinatorial aspects of partitions of integers (05A17) Polynomials in number theory (11C08) Fourier coefficients of automorphic forms (11F30) Dedekind eta function, Dedekind sums (11F20) Special sequences and polynomials (11B83)

Related Items (14)

On a conjecture of Heim and Neuhauser on some polynomials arising from modular forms and related to Fibonacci polynomials ⋮ Variations of central limit theorems and Stirling numbers of the first kind ⋮ Horizontal and vertical log-concavity ⋮ Polynomization of the Liu-Zhang inequality for the overpartition function ⋮ The irreducibility of polynomials related to work of Heim, Luca and Neuhauser ⋮ Zeros transfer for recursively defined polynomials ⋮ Estimate for the largest zeros of the D'Arcais polynomials ⋮ Congruences and integral roots of D'Arcais polynomials ⋮ Solving third-order linear recurrence relations with applications to number theory and combinatorics ⋮ Inequalities for plane partitions ⋮ Zeros of recursively defined polynomials ⋮ Difference equations related to number theory ⋮ On the growth and zeros of polynomials attached to arithmetic functions ⋮ Proof of the Bessenrodt-Ono inequality by induction

Cites Work

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• Fourier coefficients of powers of the Dedekind eta function
• Polynomials with real zeros and Pólya frequency sequences
• On cyclotomic factors of polynomials related to modular forms
• The vanishing of Ramanujan's function \(\tau(n)\)
• The Classical Orthogonal Polynomials
• A generalization of a second irreducibility theorem of I. Schur
• Imaginary Powers of the Dedekind Eta Function

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