Higher order Turán inequalities for the distinct partition function

被引：1

作者：

Dong, Janet J. W. ^{[1
]}

Ji, Kathy Q. ^{[1
]}

机构：

[1] Tianjin Univ, Ctr Appl Math, Tianjin 300072, Peoples R China

来源：

JOURNAL OF NUMBER THEORY | 2024年 / 260卷

基金：

美国国家科学基金会;

关键词：

Log-concavity; The third-order Tur & aacute; n inequalities; Partitions into distinct parts; The first modified Bessel function of; the first kind; JENSEN POLYNOMIALS; LOG-CONCAVITY; NUMBER; TURAN;

D O I：

10.1016/j.jnt.2024.01.002

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We prove that the number q(n) of partitions of n with distinct parts is log -concave for n >= 33 and satisfies the third -order Tur & aacute;n inequalities for n >= 121 conjectured by Craig and Pun. In doing so, we establish explicit error terms for q(n) and for q(n - 1)q(n +1)/q(n)(2) based on Chern's asymptotic formulas for eta-quotients.

引用

页码：71 / 102

页数：32

共 30 条

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