On the number of prime factors of an integer

DOI10.1215/S0012-7094-88-05620-7zbMath0655.10036OpenAlexW2062731724MaRDI QIDQ1109069

Adolf Hildebrand, Gérald Tenenbaum

Publication date: 1988

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

Full work available at URL: https://doi.org/10.1215/s0012-7094-88-05620-7

zbMATH Keywords

asymptotic formulasaddle-point methodnumber of distinct prime factors

Mathematics Subject Classification ID

Distribution of primes (11N05)

Related Items (22)

Upper bound of the local law for certain additive functions ⋮ On the representation of an integer as the sum of a large and a small square ⋮ Sur le nombre des entiers sans grand facteur premier. (On the number of integers without large prime factor) ⋮ Remarques sur un théorème de G. Halász et A. Sárközy ⋮ An asymptotic expansion related to the Dickman function ⋮ Quelques exemples de suites unimodales en théorie des nombres ⋮ On the gaps in multiplicatively closed sets generated by at most two elements ⋮ Unimodality of the distribution of the number of prime divisors of an integer ⋮ A Hardy-Ramanujan-type inequality for shifted primes and sifted sets ⋮ The distribution of numbers with many ordered factorizations ⋮ Congruences and rational exponential sums with the Euler function ⋮ On an almost-prime sieve ⋮ On factorizations into coprime parts ⋮ On local laws for the number of small prime factors ⋮ On the distribution of the values of arithmetic functions. The number of prime factors of an integer ⋮ Unnamed Item ⋮ Additive problems for integers with a given number of prime divisors ⋮ On the eigenstructure of sparse matrices related to the prime number theorem ⋮ Double exponential lower bound for the number of representations of unity by Egyptian fractions ⋮ PRIME DIVISORS ARE POISSON DISTRIBUTED ⋮ On the distribution of integers with a fixed number of prime factors ⋮ The local behaviour of some additive functions

Cites Work

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• On the integers having exactly \(k\) prime factors
• The Distribution of Round Numbers
• On Integers Free of Large Prime Factors
• On the distribution of integers with a given number of prime factors
• Sur la distribution des nombres entiers ayant une quantité fixée de facteurs premiers

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