Odd values of the Ramanujan $\tau$-function

DOI10.24033/bsmf.2083zbMath0635.10020OpenAlexW2585698211MaRDI QIDQ3773954

V. Kumar Murty, M. Ram Murty, Tarlok N. Shorey

Publication date: 1987

Published in: Bulletin de la Société mathématique de France (Search for Journal in Brave)

Full work available at URL: http://www.numdam.org/item?id=BSMF_1987__115__391_0

zbMATH Keywords

linear forms in logarithmsBaker's methodFourier coefficientRamanujan tau-functiondiophantine analysisAtkin-Serre conjecturecusp form of weight 12

Mathematics Subject Classification ID

Asymptotic results on arithmetic functions (11N37) Fourier coefficients of automorphic forms (11F30) Holomorphic modular forms of integral weight (11F11) Higher degree equations; Fermat's equation (11D41) Approximation to algebraic numbers (11J68)

Related Items (18)

Variations of Lehmer's conjecture for Ramanujan's tau-function ⋮ Odd values of the Ramanujan tau function ⋮ Even values of Ramanujan's tau-function ⋮ Odd prime values of the Ramanujan tau function ⋮ A central limit theorem for Ramanujan's tau function ⋮ A short note on inadmissible coefficients of weight 2 and \(2k+1\) newforms ⋮ Analytic number theory. Abstracts from the workshop held November 6--12, 2022 ⋮ Variants of Lehmer's speculation for newforms ⋮ Polynomial interpolation of modular forms for Hecke groups ⋮ On the largest prime factor of non-zero Fourier coefficients of Hecke eigenforms ⋮ On values of Ramanujan's tau function involving two prime factors ⋮ On the prime factors of the iterates of the Ramanujan τ–function ⋮ Hyperelliptic curves and newform coefficients ⋮ Distinguishing newforms by their Hecke eigenvalues ⋮ A note on lower bounds of heights of non-zero Fourier coefficients of Hilbert cusp forms ⋮ Some remarks on small values of \(\tau (n)\) ⋮ On \(L\)-functions of modular elliptic curves and certain \(K3\) surfaces ⋮ Fourier coefficients of level 1 Hecke eigenforms

Cites Work

• Divisibilite de certaines fonctions arithmétiques
• Гиперэллиптическое диофантово уравнение и числа классов идеалов
• A sharpening of the bounds for linear forms in logarithms
• A sharpening of the bounds for linear forms in logarithms II
• Rational approximations to algebraic numbers

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