Congruences on sums of q-binomial coefficients

Congruences on sums of q-binomial coefficients

We establish a q-analogue of Sun–Zhao's congruence on harmonic sums. Based on this q-congruence and a q-series identity, we prove a congruence conjecture on sums of central q-binomial coefficients, which was recently proposed by Guo. We also deduce a q-analogue of a congruence due to Apagodu an...

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Veröffentlicht in:Advances in applied mathematics 2020-05, Vol.116, p.102003, Article 102003
Hauptverfasser: Liu, Ji-Cai, Petrov, Fedor
Format: Artikel
Sprache:eng
Schlagworte:
Cyclotomic polynomials
Mathematics
Mathematics, Applied
Physical Sciences
q-Binomial coefficients
q-Congruences
Science & Technology
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Zusammenfassung:We establish a q-analogue of Sun–Zhao's congruence on harmonic sums. Based on this q-congruence and a q-series identity, we prove a congruence conjecture on sums of central q-binomial coefficients, which was recently proposed by Guo. We also deduce a q-analogue of a congruence due to Apagodu and Zeilberger from Guo's q-congruence.
ISSN:0196-8858
1090-2074
DOI:10.1016/j.aam.2020.102003