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http://arxiv.org/pdf/1901.0784...
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arXiv.org e-Print Archive
Preprint . 2019
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Congruences for q-Binomial Coefficients

descriptionPublicationkeyboard_double_arrow_right Part of book or chapter of book , Article , Preprint , Other literature type 11 Nov 2019Embargo end date: 01 Jan 2019 English Publisher:Springer International Publishing
Authors: Zudilin, W.;

doi: 10.1007/978-3-030-57050-7_41 , 10.48550/arxiv.1901.07843

arXiv: http://arxiv.org/abs/1901.07843

handle: 2066/239830

Congruences for q-Binomial Coefficients

Abstract

We discuss $q$-analogues of the classical congruence $\binom{ap}{bp}\equiv\binom{a}{b}\pmod{p^3}$, valid for primes $p>3$, as well as its generalisations. In particular, we prove related congruences for ($q$-analogues of) integral factorial ratios.

12 pages

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Keywords

Mathematics - Number Theory, Mathematics - Classical Analysis and ODEs, Mathematics - Quantum Algebra, Classical Analysis and ODEs (math.CA), FOS: Mathematics, Trends in Mathematics, Mathematics - Combinatorics, Quantum Algebra (math.QA), 11B65 (Primary), 05A10, 11A07 (Secondary), Number Theory (math.NT), Combinatorics (math.CO), Mathematics

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citations
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
29
Top 10%
Top 10%
Top 10%
Green
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