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

Author:

Kim Byungchan1,Kim Eunmi2ORCID,Lovejoy Jeremy3

Affiliation:

1. School of Liberal Arts, Seoul National University of Science and Technology, 232 Gongneung-ro, Nowon-gu, Seoul 01811, Republic of Korea

2. Institute of Mathematical Sciences, Ewha Womans University, 52 Ewhayeodae-gil, Seodaemun-gu, Seoul 03760, Republic of Korea

3. Centre National de la Recherche Scientifique, Université Denis Diderot — Paris 7, Case 7014, 75205 Paris Cedex 13, France

Abstract

Motivated by certain [Formula: see text]-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 [Formula: see text]-series transformations and Ingham’s Tauberian theorem.

Funder

Ministry of Education

Ministry of Science and ICT

Publisher

World Scientific Pub Co Pte Lt

Subject

Algebra and Number Theory

Cited by 4 articles. 订阅此论文施引文献 订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献

1. A Unified Treatment of Families of Partition Functions;La Matematica;2024-09-05

2. Some Results for Bipartition Difference Functions;Annals of Combinatorics;2024-03-01

3. Positive differences of overpartitions with separated parts;The Ramanujan Journal;2023-12-28

4. THEOREMS OF LEGENDRE TYPE FOR OVERPARTITIONS;Bulletin of the Australian Mathematical Society;2023-04-28

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