On weighted overpartitions related to some q -series in Ramanujan's lost notebook

Byungchan Kim; Eunmi Kim; Jeremy Lovejoy

doi:10.1142/S1793042120400345

On weighted overpartitions related to some q -series in Ramanujan's lost notebook

Byungchan Kim, Eunmi Kim, Jeremy Lovejoy

School of Natural Sciences

Research output: Contribution to journal › Article › peer-review

8 Scopus citations

Abstract

Motivated by certain q-series of Ramanujan, we examine two overpartition difference functions. We give both combinatorial and asymptotic formulas for the differences and show that they are always positive. We also briefly discuss similar differences for some other types of partitions. Our main tools are elementary q-series transformations and Ingham's Tauberian theorem.

Original language	English
Pages (from-to)	603-619
Number of pages	17
Journal	International Journal of Number Theory
Volume	17
Issue number	3
DOIs	https://doi.org/10.1142/S1793042120400345
State	Published - Apr 2021

Keywords

asymptotics
inequalities
overpartitions
Partitions
q -series

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10.1142/S1793042120400345

Cite this

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title = "On weighted overpartitions related to some q -series in Ramanujan's lost notebook",

abstract = "Motivated by certain q-series of Ramanujan, we examine two overpartition difference functions. We give both combinatorial and asymptotic formulas for the differences and show that they are always positive. We also briefly discuss similar differences for some other types of partitions. Our main tools are elementary q-series transformations and Ingham's Tauberian theorem.",

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AB - Motivated by certain q-series of Ramanujan, we examine two overpartition difference functions. We give both combinatorial and asymptotic formulas for the differences and show that they are always positive. We also briefly discuss similar differences for some other types of partitions. Our main tools are elementary q-series transformations and Ingham's Tauberian theorem.

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KW - inequalities

KW - overpartitions

KW - Partitions

KW - q -series

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JO - International Journal of Number Theory

JF - International Journal of Number Theory

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ER -

On weighted overpartitions related to some q -series in Ramanujan's lost notebook

Abstract

Keywords

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