Log-concavity results for a biparametric and an elliptic extension of the q-binomial coefficients

Abstract

We establish discrete and continuous log-concavity results for a biparametric extension of the [Formula: see text]-numbers and of the [Formula: see text]-binomial coefficients. By using classical results for the Jacobi theta function we are able to lift some of our log-concavity results to the elliptic setting. One of our main ingredients is a putatively new lemma involving a multiplicative analogue of Turán’s inequality.