Prime divisors of Fourier coefficients of modular forms

DOI10.1215/S0012-7094-84-05104-4zbMath0537.10026OpenAlexW2022545214MaRDI QIDQ792379

V. Kumar Murty, M. Ram Murty

Publication date: 1984

Published in: Duke Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1215/s0012-7094-84-05104-4

zbMATH Keywords

generalized Riemann hypothesisFourier coefficientsdivisibility propertiesnumber of distinct prime divisorsmodular forms of integral weightRamanujan \(\tau\)-function

Mathematics Subject Classification ID

Fourier coefficients of automorphic forms (11F30) Holomorphic modular forms of integral weight (11F11)

Related Items (16)

Bounded gaps between primes in Chebotarev sets ⋮ Coprimality of Fourier coefficients of eigenforms ⋮ A variant of Lehmer's conjecture ⋮ REDUCTION modp OF SUBGROUPS OF THE MORDELL–WEIL GROUP OF AN ELLIPTIC CURVE ⋮ An all-purpose Erdős-Kac theorem ⋮ On the normal number of prime factors of \(\varphi(n)\) subject to certain congruence conditions ⋮ Non-CM elliptic curves with infinitely many almost prime Frobenius traces ⋮ On the largest prime factor of non-zero Fourier coefficients of Hecke eigenforms ⋮ Cyclicity and exponents of CM elliptic curves modulo $p$ in short intervals ⋮ On the number of prime factors of \(\varphi{} (\varphi{}(n))\) ⋮ On the normal number of prime factors of sums of Fourier coefficients of eigenforms ⋮ GAUSSIAN LAWS ON DRINFELD MODULES ⋮ Distribution of Hecke eigenvalues ⋮ On the number of prime divisors and radicals of non-zero Fourier coefficients of Hilbert cusp forms ⋮ The Number of Non-cyclic Sylow Subgroups of the Multiplicative Group Modulo n ⋮ Compositions with the Euler and Carmichael functions

Cites Work

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• Das asymptotische Verhalten von Summen über multiplikative Funktionen
• Quelques applications du théorème de densité de Chebotarev
• Divisibilite de certaines fonctions arithmétiques
• Über Ramanujansche Kongruenzeigenschaften der Zerfällungsanzahlen. I
• Galois properties of points of finite order of elliptic curves

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