Effective estimates for the smallest parts function

We give a substantial improvement for the error term in the asymptotic formula for the smallest parts function spt(n) of Andrews. Our methods depend on an explicit bound for sums of Kloosterman sums of half integral weight on the full modular group.

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Bibliographic Details
Published inJournal of number theory Vol. 241; pp. 364 - 386
Main Author González, Oscar E.
Format Journal Article
LanguageEnglish
Published Elsevier Inc 01.12.2022
Subjects
Partition function
Smallest parts function
Sums of Kloosterman sums
Partition function
Sums of Kloosterman sums
Smallest parts function
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Summary:We give a substantial improvement for the error term in the asymptotic formula for the smallest parts function spt(n) of Andrews. Our methods depend on an explicit bound for sums of Kloosterman sums of half integral weight on the full modular group.
ISSN:0022-314X
1096-1658
DOI:10.1016/j.jnt.2022.03.015