• Arithmetic properties of the Ramanujan function

• # Fulltext

https://www.ias.ac.in/article/fulltext/pmsc/116/01/0001-0008

• # Keywords

Ramanujan τ-function; applications ofS-unit equations

• # Abstract

We study some arithmetic properties of the Ramanujan function τ(n), such as the largest prime divisorP (τ(n)) and the number of distinct prime divisors ω (τ (n)) of τ(n) for various sequences ofn. In particular, we show thatP(τ(n)) ≥ (logn)33/31+o(1) for infinitely many n, and$$P(\tau )(p)\tau (p^2 )\tau (p^3 )) &gt; (1 + o(1))\frac{{\log \log p\log \log \log p}}{{\log \log \log \log p}}$$ for every primep with τ(ρ) ≠ 0.

• # Author Affiliations

1. Instituto de Matemáticas, Universidad Nacional Autónoma de México, Morelia, Michoacán - C.P. 58089, México
2. Department of Computing, Macquarie University, Sydney, NSW - 2109, Australia

• # Proceedings – Mathematical Sciences

Current Issue
Volume 129 | Issue 3
June 2019