An all-purpose Erdős-Kac theorem

DOI10.1007/s00209-023-03370-yMaRDI QIDQ6060821

M. Ram Murty, V. Kumar Murty, Sudhir Pujahari

Publication date: 6 November 2023

Published in: Mathematische Zeitschrift (Search for Journal in Brave)

zbMATH Keywords

modular formcentral limit theoremRiemann hypothesisSiegel zeromethod of momentsHecke eigenformprime numberomega functionErdős-Kac theoremlocalized theorem

Mathematics Subject Classification ID

Asymptotic results on arithmetic functions (11N37) Arithmetic functions in probabilistic number theory (11K65) Applications of automorphic functions and forms to multiplicative problems (11N75)

Cites Work

• Remarks on the Fourier coefficients of modular forms
• An analogue of the Erdős-Kac theorem for Fourier coefficients of modular forms
• Prime divisors of Fourier coefficients of modular forms
• Explicit formulae and the Lang-Trotter conjecture
• Quelques applications du théorème de densité de Chebotarev
• On \(\ell\)-adic representations attached to modular forms
• A bound for the least prime ideal in the Chebotarev density theorem
• Some effective cases of the Brauer-Siegel theorem
• Effective means for complex multiplicative functions
• On the normal number of prime factors of \(\phi(n)\)
• La conjecture de Weil. I
• On the normal number of prime factors of sums of Fourier coefficients of eigenforms
• Prime analogues of the Erdős-Kac theorem for elliptic curves
• The vanishing of Ramanujan's function \(\tau(n)\)
• Distinguishing Hecke eigenforms
• IMAGES OF ADELIC GALOIS REPRESENTATIONS FOR MODULAR FORMS
• On the Distribution of Additive Number-Theoretic Functions (II)
• Modular Forms and the Chebotarev Density Theorem
• On a Theorem of Hardy and Ramanujan
• Non-Abelian Generalizations of the Erdős-Kac Theorem
• On the Central Limit Theorem for the Prime Divisor Function
• Probability methods in some problems of analysis and number theory
• On the Distribution of Additive Number-Theoretic Functions
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