Integers, without large prime factors, in arithmetic progressions. I

DOI10.1007/BF02392787zbMath0784.11045OpenAlexW2068484936MaRDI QIDQ1309360

Andrew Granville

Publication date: 9 March 1994

Published in: Acta Mathematica (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf02392787

zbMATH Keywords

uniformityarithmetic progressionintegers without large prime factorsDickman functionBombieri-Vinogradov type result

Mathematics Subject Classification ID

Distribution of integers with specified multiplicative constraints (11N25)

Related Items (12)

On a conjecture of Soundararajan ⋮ Smooth numbers and the Dickman \(\rho\) function ⋮ Rigorous analysis of a randomised number field sieve ⋮ Numbers in a given set with (or without) a large prime factor ⋮ Smooth values of shifted primes in arithmetic progressions ⋮ The Distribution of Smooth Numbers in Arithmetic Progressions ⋮ Character sums with exponential functions over smooth numbers ⋮ An interval result for the number field \(\psi{}(x,y)\) function ⋮ Some remarks on nonnegative multiplicative functions on arithmetic progressions ⋮ Théorèmes de type Fouvry–Iwaniec pour les entiers friables ⋮ On the asymptotic behavior of the Dickman-de Bruijn function ⋮ Integers without large prime factors

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• On the number of positive integers \(\leq x\) and free of prime factors \(>y\)
• A property of the counting function of integers with no large prime factors
• On the number of prime factors of integers without large prime divisors
• A new iterative method in Waring's problem
• Sur le nombre des entiers sans grand facteur premier. (On the number of integers without large prime factor)
• Multiplicative Functions on Arithmetic Progressions
• The distribution of quadratic residues and non‐residues
• On Integers Free of Large Prime Factors
• Multiplicative functions on arithmetic progressions, II.
• Integers without large prime factors, II
• Asymptotic Estimates of Sums Involving the Moebius Function. II
• Entiers Sans Grand Facteur Premier En Progressions Arithmetiques
• The Distribution of Smooth Numbers in Arithmetic Progressions
• An improvement of Selberg's sieve method I
• Numbers with small prime factors, and the least 𝑘th power non-residue
• The Difference between Consecutive Prime Numbers
• An Elementary Proof of the Prime-Number Theorem for Arithmetic Progressions

This page was built for publication: Integers, without large prime factors, in arithmetic progressions. I