An explicit bound for the number of partitions into roots

JOURNAL OF NUMBER THEORY

卷:169

Article

Luca, Florian¹  Ralaivaosaona, Dimbinaina² 

[1] Univ Witwatersrand, Sch Math, Private Bag X3, ZA-2050 Johannesburg, South Africa

[2] Univ Stellenbosch, Dept Math Sci, Private Bag X1, ZA-7602 Matieland, South Africa

关键词: Asymptotic estimate;    Integer partition;    Mellin transform;    Saddle point method;   

DOI  :  10.1016/j.jnt.2016.05.017

来源: Elsevier

【 摘 要 】

We use the saddle point method to prove an explicit upper bound for the number of representations of a positive integer n into the form left perpendicular root a(1)right perpendicular + left perpendicular root a(2)right perpendicular + ... + left perpendicular root a(k)right perpendicular, where k and a(1), a(2), ... , a(k) are positive integers. We also give an asymptotic formula for this number as n -> infinity. (C) 2016 Elsevier Inc. All rights reserved.

【 授权许可】

Free