Recurrence relations for polynomials obtained by arithmetic functions-Reference-Cited by-同舟云学术

Recurrence relations for polynomials obtained by arithmetic functions

Published:2019-07 Issue:06 Volume:15 Page:1291-1303
ISSN:1793-0421
Container-title:International Journal of Number Theory
language:en
Short-container-title:Int. J. Number Theory

Author:

Heim Bernhard¹,Luca Florian²³⁴,Neuhauser Markus⁵⁶

Affiliation:

1. German University of Technology in Oman (GUtech), P. O. Box 1816, Athaibah PC 130, Sultanate of Oman

2. School of Mathematics, University of the Witwatersrand, Private Bag 3, Wits 2050, Johannesburg, South Africa

3. Max-Planck-Institute for Mathematics, Vivatsgasse 7, 53111 Bonn, Germany

4. Department of Mathematics, Faculty of Sciences, University of Ostrava, 30 Dubna 22, 701 03 Ostrava 1, Czech Republic

5. German University of Technology in Oman (GUtech), P. O. Box 1816, Athaibah PC 130, Sultanate of Oman

6. Faculty of Mathematics, Computer Science, and Natural Sciences, RWTH Aachen University, 52056 Aachen, Germany

Abstract

Families of polynomials associated to arithmetic functions [Formula: see text] are studied. The case [Formula: see text], the divisor sum, dictates the non-vanishing of the Fourier coefficients of powers of the Dedekind eta function. The polynomials [Formula: see text] are defined by [Formula: see text]-term recurrence relations. For the case that [Formula: see text] is a polynomial of degree [Formula: see text], we prove that at most a [Formula: see text] term recurrence relation is needed. For the special case [Formula: see text], we obtain explicit formulas and results.

Publisher

World Scientific Pub Co Pte Lt

Subject

Algebra and Number Theory

Link

https://www.worldscientific.com/doi/pdf/10.1142/S1793042119500726

Reference12 articles.

1. A generalization of a second irreducibility theorem of I. Schur

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