An explicit bound for the number of partitions into roots

作者：Luca Florian; Ralaivaosaona Dimbinaina

来源：Journal of Number Theory, 2016, 169: 250-264.

DOI：10.1016/j.jnt.2016.05.017

• Asymptotic estimate
• Integer partition
• Mellin transform
• Saddle point method

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.

• 出版日期2016-12