ODD VALUES OF FOURIER COEFFICIENTS OF CERTAIN MODULAR FORMS

DOI10.1142/S1793042107001036zbMath1197.11056WikidataQ114072062 ScholiaQ114072062MaRDI QIDQ5386810

V. Kumar Murty, M. Ram Murty

Publication date: 14 May 2008

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

zbMATH Keywords

congruencesFourier coefficientsModular formsLang--Trotter conjecture

Mathematics Subject Classification ID

Congruences for modular and (p)-adic modular forms (11F33) Fourier coefficients of automorphic forms (11F30) Holomorphic modular forms of integral weight (11F11) Linear forms in logarithms; Baker's method (11J86)

Related Items (13)

Odd values of the Ramanujan tau function ⋮ Sign changes and nonvanishing of Fourier coefficients of holomorphic cusp forms ⋮ Gaps between nonzero Fourier coefficients of cusp forms ⋮ Simultaneous non-vanishing and sign changes of Fourier coefficients of modular forms ⋮ Variants of Lehmer's speculation for newforms ⋮ On the largest prime factor of non-zero Fourier coefficients of Hecke eigenforms ⋮ The first simultaneous sign change and non-vanishing of Hecke eigenvalues of newforms ⋮ Fourier coefficients of forms of CM-type ⋮ Distinguishing newforms by their Hecke eigenvalues ⋮ A note on lower bounds of heights of non-zero Fourier coefficients of Hilbert cusp forms ⋮ Uniqueness of Fourier coefficients of eigenforms ⋮ Random ordering in modulus of consecutive Hecke eigenvalues of primitive forms ⋮ On the number of prime divisors and radicals of non-zero Fourier coefficients of Hilbert cusp forms

Cites Work

• Diophantine approximations and value distribution theory
• Frobenius distributions in \(\mathrm{GL}_2\)-extensions. Distribution of Frobenius automorphisms in \(\mathrm{GL}_2\)-extensions of the rational numbers
• Another congruence for the Apéry numbers
• La conjecture de Weil. I
• On the geometry and arithmetic of some Siegel modular threefolds
• An upper bound for the size of integral solutions to \(Y^ m= f(X)\)
• Modularity of a certain Calabi-Yau threefold
• Über Modulfunktionen und die Dirichletschen Reihen mit Eulerscher Produktentwicklung. I
• The vanishing of Ramanujan's function \(\tau(n)\)
• Modular Forms and the Chebotarev Density Theorem
• 2-ADIC PROPERTIES OF CERTAIN MODULAR FORMS AND THEIR APPLICATIONS TO ARITHMETIC FUNCTIONS

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