Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
8900235 | Journal of Mathematical Analysis and Applications | 2018 | 26 Pages |
Abstract
Let fâZ[y] be a polynomial such that f(N)âN, and let pAf(n) denote number of partitions of n whose parts lie in the set Af:={f(n):nâN}. Under hypotheses on the roots of fâf(0), we use the Hardy-Littlewood circle method, a polylogarithm identity, and the Matsumoto-Weng zeta function to derive asymptotic formulae for pAf(n) as n tends to infinity. This generalises asymptotic formulae for the number of partitions into perfect dth powers, established by Vaughan for d=2, and Gafni for the case dâ¥2, in 2015 and 2016 respectively.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Analysis
Authors
Alexander Dunn, Nicolas Robles,