On Ramanujan's tau function
type: Item
instance of: scholarly article
title: On Ramanujan's tau function
zbMATH Open document ID: 0942.11007
published in: Rocky Mountain Journal of Mathematics
publication date: 1999-06-28T00:00:00Z
full work available at URL: cont282.html
review text: Ramanujan's function \(\tau(n)\) is defined by \[ \sum_1^\infty \tau(n) x^n= x\prod_1^\infty (1-x^n)^{24}, \qquad |x|<1. \] The author gives a new representation of \(\tau(n)\), which contains finite sums of values of \(\sigma_3\) (3rd powers divisor function) and \(r_8\) (number of sums of 8 squares). He deduces a congruence \(\operatorname {mod}16\) of \(\tau(n)\).
reviewed by: Jürgen Spilker
Mathematics Subject Classification ID: 11A25
Mathematics Subject Classification ID: 11B75
zbMATH DE Number: 1309725
zbMATH Keywords: arithmetic functions
zbMATH Keywords: Ramanujan's tau-function
zbMATH Keywords: representation
zbMATH Keywords: congruence
author: John A. Ewell
MaRDI profile type: Publication
OpenAlex ID: W2019291583
cites work: Two Congruence Properties of Ramanujan's Function τ(n )
cites work: A Formula for Ramanujan's Tau Function
cites work: Arithmetical consequences of a sextuple product identity
cites work: Q3259107
DOI: 10.1216/RMJM/1181071781
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description: scientific article; zbMATH DE number 1309725