Periodicity of signs of Fourier coefficients of eta-quotients

Byungchan Kim

doi:10.1016/j.jmaa.2011.07.021

Periodicity of signs of Fourier coefficients of eta-quotients

Byungchan Kim

School of Natural Sciences

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

5 Scopus citations

Abstract

We study the periodicity of signs of Fourier coefficients of the function,. where αis a positive integer, f(-q)=Πn=1∞(1-qn), and rd∈Z. As an application, we will prove the periodicity of signs for the crank differences conjectured by G.E. Andrews and R. Lewis and for the weighted counts of certain types of partitions.

Original language	English
Pages (from-to)	998-1004
Number of pages	7
Journal	Journal of Mathematical Analysis and Applications
Volume	385
Issue number	2
DOIs	https://doi.org/10.1016/j.jmaa.2011.07.021
State	Published - 15 Jan 2012

Keywords

Circle method
Eta-quotients
Integer partitions
Periodicity for the sign changes

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10.1016/j.jmaa.2011.07.021

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abstract = "We study the periodicity of signs of Fourier coefficients of the function,. where αis a positive integer, f(-q)=Πn=1∞(1-qn), and rd∈Z. As an application, we will prove the periodicity of signs for the crank differences conjectured by G.E. Andrews and R. Lewis and for the weighted counts of certain types of partitions.",

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AB - We study the periodicity of signs of Fourier coefficients of the function,. where αis a positive integer, f(-q)=Πn=1∞(1-qn), and rd∈Z. As an application, we will prove the periodicity of signs for the crank differences conjectured by G.E. Andrews and R. Lewis and for the weighted counts of certain types of partitions.

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KW - Eta-quotients

KW - Integer partitions

KW - Periodicity for the sign changes

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EP - 1004

JO - Journal of Mathematical Analysis and Applications

JF - Journal of Mathematical Analysis and Applications

IS - 2

ER -

Periodicity of signs of Fourier coefficients of eta-quotients

Abstract

Keywords

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