Twin Nicomachean q-identities and conjectures for the associated discriminants, polynomials, and inequalities

DOI10.1142/S1793042120400175zbMath1498.11065OpenAlexW3080773315WikidataQ123215250 ScholiaQ123215250MaRDI QIDQ4991697

Seon-Hong Kim, Kenneth B. Stolarsky

Publication date: 3 June 2021

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

Full work available at URL: https://doi.org/10.1142/s1793042120400175

zbMATH Keywords

partitions\(q\)-analogueszeros of polynomialsdiscriminantspower meanssums of cubesmolien seriesNicomachean identitysquared triangular numbers

Mathematics Subject Classification ID

Binomial coefficients; factorials; (q)-identities (11B65) Zeros of polynomials, rational functions, and other analytic functions of one complex variable (e.g., zeros of functions with bounded Dirichlet integral) (30C15) Elementary theory of partitions (11P81) Special sequences and polynomials (11B83)

Cites Work

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• Explicit formulas for Vasil'ev invariants of the fourth order for knots
• On the {\(q\)}-analogue of the sum of cubes
• {\(q\)}-analogues of the sums of consecutive integers, squares, cubes, quarts and quints
• Shanks' convergence acceleration transform, Padé approximants and partitions
• The Power Mean and the Logarithmic Mean
• Inequalities and Identities for Sums and Integrals
• Error-Correcting Codes and Invariant Theory: New Applications of a Nineteenth-Century Technique
• A VARIATION ON THE THEME OF NICOMACHUS
• Differentiation evens out zero spacings

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