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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 Turán's inequality.

preprint2020arXivOpen access
Michael J. SchlosserKoushik SenapatiAli K. Uncu
math.COmath.CA
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Michael J. SchlosserKoushik SenapatiAli K. Uncu

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