Congruences for $q$-binomial coefficients

Abstract

We discuss $q$-analogues of the classical congruence $\left(\genfrac{}{}{0ex}{}{ap}{bp}\right)\equiv \left(\genfrac{}{}{0ex}{}{a}{b}\right)(\mathrm{mod}{p}^3)$, 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

References in corpus (2)

• A q-rious positivity
• Congruences modulo cyclotomic polynomials and algebraic independence for $q$-series

Cited by in corpus (2)

• Congruences on sums of $q$-binomial coefficients
• Dwork-type supercongruences through a creative $q$-microscope