Ramanujan’s Tau-Function in Terms of Bell Polynomials
R. Sivaraman1, H. N. Núñez-Yépez2, J. López-Bonilla3
1Dr. R. Sivaraman, Department of Mathematics, Dwaraka Doss Goverdhan Doss Vaishnav College, Chennai (Tamil Nadu), India.
2H. N. Núñez-Yépez, Departamento de Física, Universidad Autónoma Metropolitana-Iztapalapa, Apdo. Postal 55-534, Iztapalapa CP 09340, CDMX, México.
3Prof. J. López-Bonilla, ESIME-Zacatenco, Instituto Politécnico Nacional, Edif. 4, 1er. Piso, Col. Lindavista CP 0778, CDMX, México.
Manuscript received on 15 August 2023 | Revised Manuscript received on 07 September 2023 | Manuscript Accepted on 15 October 2023 | Manuscript published on 30 October 2023 | PP: 1-3 | Volume-3 Issue-2, October 2023 | Retrieval Number: 100.1/ijam.B1157103223 | DOI: 10.54105/ijam.B1157.103223
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Abstract: We obtain a recurrence relation for the Ramanujan’s tau-function involving the sum of divisors function, and the solution of this recurrence gives a closed formula for 𝝉(𝒏) in terms of the complete Bell polynomials.
Keywords: Sum of divisors function, Color partitions, Recurrence relations, Complete Bell polynomials, Ramanujan’s function 𝝉(𝒏).
Scope of the Article: Number Theory