Elementary Proof of Lehmer's Conjecture on Non-vanishing of Tau Function

2015/06/06 by Will Y. Lee, Lee, Will Y.
Mathematics · #Advanced Algebra and Geometry #Advanced Mathematical Identities #Analytic Number Theory Research #FOS: Mathematics #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.1506.02098

openalex publication_date 2015/06/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper we prove Lehmer's conjecture on Ramanujan's tau function, namely tau(n) not equal to zero for n >= 1 by investigating the additive group structure attached to tau(n) with the aid of the pigeonhole principle and unique factorization theorem.

Related

• Lehmer's Conjecture on the Non-vanishing of Ramanujan's Tau Function
• Variations of Lehmer's Conjecture for Ramanujan's tau-function
• On some values which do not belong to the image of Ramanujan's tau-function
• Some Remarks on Small Values of τ(n)
• Proof of the Lehmer conjecture on Ramanujan's τ function