Talk: A q-analog of Ljunggren's binomial congruence (Illinois)

Date: 2012/10/13
Occasion: Midwest Number Theory Conference for Graduate Students and Recent PhDs IX
Place: University of Illinois at Urbana-Champaign

Abstract

Ljunggren's congruence states that $\binom{ap}{bp}$ is congruent to $\binom{a}{b}$ modulo $p^3$. The goal of this talk is to extend this congruence into the q-world. To this end, the q-binomial coefficients are reviewed and characterized in a variety of ways.

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