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On the prime factors of the iterates of the Ramanujan τ–function

Part of: Diophantine approximation, transcendental number theory Sequences and sets

Published online by Cambridge University Press:  11 November 2020

Florian Luca ,
Sibusiso Mabaso  and
Pantelimon Stănică
Florian Luca
Affiliation:
School of Mathematics, University of the Witwatersrand, Private Bag X3, Wits 2050, Johannesburg, South Africa Max Planck Institute for Software Systems, Saarbrücken, Germany Research Group in Algebraic Structures and Applications, King Abdulaziz University, Jeddah, Saudi Arabia Centro de Ciencias Matemáticas, UNAM, Morelia, Mexico (Florian.Luca@wits.ac.za)
Sibusiso Mabaso
Affiliation:
Mangosuthu University of Technology, 511 Griffiths Mxenge Hwy, Umlazi, Durban4301, South Africa (ASmabaso@mut.ac.za)
Pantelimon Stănică
Affiliation:
Applied Mathematics Department, Naval Postgraduate School, Monterey, CA93943–5216, USA (pstanica@nps.edu)
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Abstract

In this paper, for a positive integer n ≥ 1, we look at the size and prime factors of the iterates of the Ramanujan τ function applied to n.

Keywords

Ramanujan τ-functiondiophantine equations

MSC classification

Primary: 11B39: Fibonacci and Lucas numbers and polynomials and generalizations
Secondary: 11J86: Linear forms in logarithms; Baker's method
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 63 , Issue 4 , November 2020 , pp. 1031 - 1047
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Copyright
Copyright © The Author(s), 2020. Published by Cambridge University Press on Behalf of The Edinburgh Mathematical Society

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