ON RAMANUJAN’S TAU-FUNCTION

Print ISSN: 2319-1023 | Online ISSN: 2582-5461 | Total Downloads : 65

Volume : 11 , Issue : 1
DOI: https://doi.org/10.56827/JRSMMS.2023.1101.4
Author :
J. López-Bonilla (ESIME-Zacatenco Instituto Politécnico Nacional Edif. 4, 1er. Piso, Col. Lindavista CP 07738, CDMX, MEXICO)
S. Vidal-Beltrán (ESIME-Zacatenco Instituto Politécnico Nacional Edif. 4, 1er. Piso, Col. Lindavista CP 07738, CDMX, MEXICO)
R. Rajendra (Department of Mathematics, Field Marshal K. M. Cariappa College, Madikeri - 571201, INDIA)
P. Siva Kota Reddy (Department of Mathematics, JSS Science and Technology University, Mysuru - 570006, INDIA)

Abstract

We exhibit a recurrence relation for the Ramanujan’s tau-function involving the sum of divisors function, whose solution gives a closed formula for $\tau(n)$ in terms of complete Bell polynomials. Besides, we show that it is possible to write $\tau(n)$ in terms of the compositions of $n$.

Keywords and Phrases

$Z$-transform, Sum of divisors function, Recurrence relations, Ramanujan’s function $\tau(n)$, Complete Bell polynomials, Color partitions, Compositions.

A.M.S. subject classification

11A25, 33-XX.

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