Congruences for $q$-binomial coefficients

Wadim Zudilin

doi:10.1007/s00026-019-00461-8

Congruences for $q$-binomial coefficients

Number Theory 2019-12-16 v2 Classical Analysis and ODEs Combinatorics Quantum Algebra

Authors: Wadim Zudilin

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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.

Keywords

congruences and supercongruences q-series and q-analogues

Cite

@article{arxiv.1901.07843,
  title  = {Congruences for $q$-binomial coefficients},
  author = {Wadim Zudilin},
  journal= {arXiv preprint arXiv:1901.07843},
  year   = {2019}
}

Comments

12 pages

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