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.

中文翻译：

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q-二项式系数的双参数和椭圆扩展的对数凹度结果

我们建立离散和连续对数凹度结果，用于q-数字和q-二项式系数。通过使用 Jacobi theta 函数的经典结果，我们能够将我们的一些对数凹度结果提升到椭圆设置。我们的主要成分之一是一个假定的新引理，涉及图兰不等式的乘法模拟。