[Sur les sommes d’Erdős de presque premiers]
En 1935, Erdős a prouvé que les sommes
In 1935, Erdős proved that the sums
Our main result gives an asymptotic for
Révisé le :
Accepté le :
Publié le :
DOI : 10.5802/crmath.650
Keywords: Almost primes, primitive set, Dickman distribution, recursive distributional equation
Mots-clés : Nombres presque premiers, ensemble primitif, loi de Dickman, équation en loi récursive
Ofir Gorodetsky 1, 2 ; Jared Duker Lichtman 3 ; Mo Dick Wong 4

@article{CRMATH_2024__362_G12_1571_0, author = {Ofir Gorodetsky and Jared Duker Lichtman and Mo Dick Wong}, title = {On {Erd\H{o}s} sums of almost primes}, journal = {Comptes Rendus. Math\'ematique}, pages = {1571--1596}, publisher = {Acad\'emie des sciences, Paris}, volume = {362}, year = {2024}, doi = {10.5802/crmath.650}, zbl = {07949973}, language = {en}, }
Ofir Gorodetsky; Jared Duker Lichtman; Mo Dick Wong. On Erdős sums of almost primes. Comptes Rendus. Mathématique, Volume 362 (2024), pp. 1571-1596. doi : 10.5802/crmath.650. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.650/
[1] Higher Mertens constants for almost primes, J. Number Theory, Volume 234 (2022), pp. 448-475 | DOI | MR | Zbl
[2] Optimal primitive sets with restricted primes, Integers, Volume 13 (2013), A69, 10 pages | MR | Zbl
[3] A probabilistic approach to a differential-difference equation arising in analytic number theory, Math. Comput., Volume 27 (1973), pp. 197-203 | DOI | MR | Zbl
[4] A generalization of primitive sets and a conjecture of Erdős, Discrete Anal., Volume 2020 (2020), 16, 13 pages | DOI | MR | Zbl
[5] On the critical exponent for
[6] Note on Sequences of Integers No One of Which is Divisible By Any Other, J. Lond. Math. Soc., Volume 10 (1935) no. 2, pp. 126-128 | DOI | MR | Zbl
[7] On the number of prime factors in integers, Acta Sci. Math., Volume 42 (1980) no. 3-4, pp. 237-246 | MR | Zbl
[8] Quickselect and the Dickman function, Comb. Probab. Comput., Volume 11 (2002) no. 4, pp. 353-371 | DOI | MR | Zbl
[9] Euler’s constant: Euler’s work and modern developments, Bull. Am. Math. Soc., Volume 50 (2013) no. 4, pp. 527-628 | DOI | MR | Zbl
[10] Almost primes and the Banks–Martin conjecture, J. Number Theory, Volume 211 (2020), pp. 513-529 | DOI | MR | Zbl
[11] Mertens’ prime product formula, dissected, Integers, Volume 21A (2021) no. Ron Graham Memorial Volume, A17, 15 pages | MR | Zbl
[12] Translated sums of primitive sets, C. R. Math. Acad. Sci. Paris, Volume 360 (2022), pp. 409-414 | DOI | Numdam | MR | Zbl
[13] A proof of the Erdős primitive set conjecture, Forum Math. Pi, Volume 11 (2023), e18, 21 pages | DOI | MR | Zbl
[14] The Dickman–Goncharov distribution, Russ. Math. Surv., Volume 75 (2020) no. 6, pp. 1089-1132 | DOI | Zbl
[15] Random minimal directed spanning trees and Dickman-type distributions, Adv. Appl. Probab., Volume 36 (2004) no. 3, pp. 691-714 | DOI | MR | Zbl
[16] On a problem of Erdős concerning primitive sequences, Math. Comput., Volume 60 (1993) no. 202, pp. 827-834 | DOI | MR | Zbl
Cité par Sources :
Commentaires - Politique