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    • 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$$P(\tau )(p)\tau (p^2 )\tau (p^3 )) > (1 + o(1))\frac{{\log \log p\log \log \log p}}{{\log \log \log \log p}}$$ for every primep with τ(ρ) ≠ 0.

    • Author Affiliations


      Florian Luca1 Igor E Shparlinski2

      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
    • Dates

  • Proceedings – Mathematical Sciences | News

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      Posted on July 25, 2019

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