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Ramanujan’s partial theta series and parity in partitions

Authors :
Ae Ja Yee
Source :
The Ramanujan Journal. 23:215-225
Publication Year :
2010
Publisher :
Springer Science and Business Media LLC, 2010.

Abstract

A partial theta series identity from Ramanujan’s lost notebook has a connection with some parity problems in partitions studied by Andrews in Ramanujan J., to appear where 15 open problems are listed. In this paper, the partial theta series identity of Ramanujan is revisited and answers to Questions 9 and 10 of Andrews are provided.

Subjects

Subjects :
Euler function
Algebra and Number Theory
Ramanujan summation
Ramanujan's sum
Combinatorics
Ramanujan theta function
symbols.namesake
Number theory
ComputingMethodologies_SYMBOLICANDALGEBRAICMANIPULATION
symbols
Ramanujan tau function
Parity (mathematics)
GeneralLiterature_REFERENCE(e.g.,dictionaries,encyclopedias,glossaries)
Ramanujan prime
MathematicsofComputing_DISCRETEMATHEMATICS
Mathematics

Details

ISSN :
15729303 and 13824090
Volume :
23
Database :
OpenAIRE
Journal :
The Ramanujan Journal
Accession number :
edsair.doi...........75ccf6e6a61d128d70916437f0c95e1a
Full Text :
https://doi.org/10.1007/s11139-009-9190-0
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