Recurrence relations for polynomials obtained by arithmetic functions

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61988987%3A17310%2F19%3AA20023VU" target="_blank" >RIV/61988987:17310/19:A20023VU - isvavai.cz</a>
Result on the web
<a href="https://www.worldscientific.com/doi/abs/10.1142/S1793042119500726" target="_blank" >https://www.worldscientific.com/doi/abs/10.1142/S1793042119500726</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1142/S1793042119500726" target="_blank" >10.1142/S1793042119500726</a>

Result language
angličtina
Original language name
Recurrence relations for polynomials obtained by arithmetic functions
Original language description
Families of polynomials associated to arithmetic functions g(n) are studied. The case g(n) = sigma(n), the divisor sum, dictates the non-vanishing of the Fourier coefficients of powers of the Dedekind eta function. The polynomials P-n(g)(X) are defined by n-term recurrence relations. For the case that g(x) is a polynomial of degree d, we prove that at most a d + 2 term recurrence relation is needed. For the special case g(x) = x, we obtain explicit formulas and results.
Czech name
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Czech description
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Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
—
OECD FORD branch
10101 - Pure mathematics

Project
<a href="/en/project/GA17-02804S" target="_blank" >GA17-02804S: Properties of number sequences and their applications</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year
2019
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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