Article overview
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
$Z$-transformSum of divisors functionRecurrence relationsRamanujan’s function $\tau(n)$Complete Bell polynomialsColor partitionsCompositions.
AMS Subject Classification
11A25, 33-XX.
Reference information
How to Cite
J. López-Bonilla, S. Vidal-Beltrán, R. Rajendra, P. Siva Kota Reddy (2023). ON RAMANUJAN’S TAU-FUNCTION. Journal of Ramanujan Society of Mathematics and Mathematical Sciences, 11(1), 55-62.