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

We establish discrete and continuous log-concavity results for a biparametric extension of the q-numbers and of the q-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 Turkn's inequality.

Automated summary

In this study, discrete and continuous log-concavity results were established for a biparametric extension of the q-numbers and q-binomial coefficients. By utilizing classical results for the Jacobi theta function, some of the log-concavity results were extended to the elliptic setting. One of the main components of this analysis is a potentially new lemma involving a multiplicative analogue of Turkn's inequality.