关于p（n）和logp（n）的新不等式。

IF 0.6 3区数学 Q3 MATHEMATICS

Ramanujan Journal Pub Date : 2023-01-01 Epub Date: 2022-10-19 DOI:10.1007/s11139-022-00653-6

Koustav Banerjee, Peter Paule, Cristian-Silviu Radu, WenHuan Zeng

引用次数: 3

摘要

设p（n）表示n的分区数。给出了一个新的无限不等式族。这推广了William Chen等人的一个结果。从这个无穷大族中，导出了logp（n）的另一个无穷大不等式族。作为后一个族的应用，例如，得到了对于n≥120，p（n）2>（1+π24n3/2-1n2）p（n-1）p（n+1）。

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New inequalities for p(n) and logp(n).

Let p(n) denote the number of partitions of n. A new infinite family of inequalities for p(n) is presented. This generalizes a result by William Chen et al. From this infinite family, another infinite family of inequalities for $log p (n)$ is derived. As an application of the latter family one, for instance obtains that for $n \geq 120$ , $\begin{matrix} p {(n)}^{2} > (1 + \frac{π}{\sqrt{24} n^{3 / 2}} - \frac{1}{n^{2}}) p (n - 1) p (n + 1) . \end{matrix}$

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来源期刊

Ramanujan Journal 数学-数学

CiteScore

1.40

自引率

14.30%

发文量

133

审稿时长

6-12 weeks

期刊介绍： The Ramanujan Journal publishes original papers of the highest quality in all areas of mathematics influenced by Srinivasa Ramanujan. His remarkable discoveries have made a great impact on several branches of mathematics, revealing deep and fundamental connections. The following prioritized listing of topics of interest to the journal is not intended to be exclusive but to demonstrate the editorial policy of attracting papers which represent a broad range of interest: Hyper-geometric and basic hyper-geometric series (q-series) * Partitions, compositions and combinatory analysis * Circle method and asymptotic formulae * Mock theta functions * Elliptic and theta functions * Modular forms and automorphic functions * Special functions and definite integrals * Continued fractions * Diophantine analysis including irrationality and transcendence * Number theory * Fourier analysis with applications to number theory * Connections between Lie algebras and q-series.