An analogue of the Erdős-Kac theorem for Fourier coefficients of modular forms

zbMath0557.10033MaRDI QIDQ762204

V. Kumar Murty, M. Ram Murty

Publication date: 1984

Published in: Indian Journal of Pure \& Applied Mathematics (Search for Journal in Brave)

zbMATH Keywords

Fourier expansionRiemann hypothesisdistribution functionArtin L-functionscusp formnumber of distinct prime divisorstotal number of prime factors

Mathematics Subject Classification ID

Fourier coefficients of automorphic forms (11F30) Holomorphic modular forms of integral weight (11F11) Arithmetic functions in probabilistic number theory (11K65)

Related Items (13)

Number of prime divisors of \(\varphi_ k(n)\), where \(\varphi_ k\) is the \(k\)-fold iterative of \(\varphi\) ⋮ Coprimality of Fourier coefficients of eigenforms ⋮ A variant of Lehmer's conjecture ⋮ The Erdős-Kac theorem for polynomials of several variables ⋮ An all-purpose Erdős-Kac theorem ⋮ Distinguishing newforms by the prime divisors of their Fourier coefficients ⋮ On the number of prime factors of \(\varphi{} (\varphi{}(n))\) ⋮ Prime analogues of the Erdős-Kac theorem for elliptic curves ⋮ On an Erdős-pomerance conjecture for rank one Drinfeld modules ⋮ A Carlitz module analogue of a conjecture of Erdos and Pomerance ⋮ On the normal number of prime factors of sums of Fourier coefficients of eigenforms ⋮ Distribution of Hecke eigenvalues ⋮ The Number of Non-cyclic Sylow Subgroups of the Multiplicative Group Modulo n

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