Variations of Lehmer's conjecture for Ramanujan's tau-function

DOI10.1016/j.jnt.2020.04.009zbMath1497.11080arXiv2005.10345OpenAlexW3028060585WikidataQ113870371 ScholiaQ113870371MaRDI QIDQ2127192

Ken Ono, Jennifer S. Balakrishnan, William Craig

Publication date: 20 April 2022

Published in: Journal of Number Theory (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2005.10345

zbMATH Keywords

Lehmer's conjectureThue equationRamanujan's tau-functionprimitive divisors of Lucas sequences

Mathematics Subject Classification ID

Exponential Diophantine equations (11D61) Higher degree equations; Fermat's equation (11D41) Fibonacci and Lucas numbers and polynomials and generalizations (11B39) Linear forms in logarithms; Baker's method (11J86)

Related Items (7)

Variations of central limit theorems and Stirling numbers of the first kind ⋮ Odd values of the Ramanujan tau function ⋮ Even values of Ramanujan's tau-function ⋮ Zeros transfer for recursively defined polynomials ⋮ A short note on inadmissible coefficients of weight 2 and \(2k+1\) newforms ⋮ Variants of Lehmer's speculation for newforms ⋮ Distinguishing newforms by their Hecke eigenvalues

Uses Software

• Magma
• PARI/GP
• SageMath

Cites Work

• Unnamed Item
• Vanishing Fourier coefficients of Hecke eigenforms
• Lucas and Lehmer numbers without primitive divisor
• Effective Chabauty
• On the practical solution of the Thue equation
• Solving Thue equations of high degree
• La conjecture de Weil. II
• Ramanujan's unpublished manuscript on the partition and tau functions with proofs and commentary
• The Magma algebra system. I: The user language
• La conjecture de Weil. I
• Classical and modular approaches to exponential Diophantine equations. I: Fibonacci and Lucas perfect powers
• The vanishing of Ramanujan's function \(\tau(n)\)
• Existence of primitive divisors of Lucas and Lehmer numbers
• Classical and modular approaches to exponential Diophantine equations II. The Lebesgue–Nagell equation
• Odd values of the Ramanujan $\tau$-function
• The diophantine equation x² + C = yⁿ
• Primary cyclotomic units and a proof of Catalans conjecture
• Variants of Lehmer's speculation for newforms

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