G. Mukherjee

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math.NT2022

Higher order log-concavity of the overpartition function and its consequences

Gargi Mukherjee, Helen W. J. Zhang, Ying Zhong

Let $p ˉ (n)$ denote the overpartition function. In this paper, we study the asymptotic higher order $lo g$ -concavity property of the overpatition function in a similar framewor…

math.NT2022

Inequalities for higher order differences of the logarithm of the overpartition function and a problem of Wang-Xie-Zhang

Gargi Mukherjee

Let $p (n)$ denote the overpartition function. In this paper, our primary goal is to study the asymptotic behavior of the finite differences of the logarithm of the overp…

math.NT2022

Inequalities for the overpartition function arising from determinants

Gargi Mukherjee

Let $p (n)$ denote the overpartition funtion. This paper presents the $2$ - $lo g$ -concavity property of $p (n)$ by considering a more general inequality of the f…

math.NT2022

Log-convexity and the overpartition function

Gargi Mukherjee

Let $p (n)$ denote the overpartition function. In this paper, we obtain an inequality for the sequence $Δ^{2} lo g n - 1 p (n - 1) / (n - 1)^{α}$ which states th…