RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB
General information
Latest issue
Forthcoming papers
Archive
Impact factor
Subscription
Guidelines for authors
License agreement
Submit a manuscript

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Izv. RAN. Ser. Mat.:
Year:
Volume:
Issue:
Page:
Find






Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register


Izv. RAN. Ser. Mat., 2019, Volume 83, Issue 1, Pages 192–202 (Mi izv8711)  

On integers whose number of prime divisors belongs to a given residue class

M. E. Changaab

a Steklov Mathematical Institute of Russian Academy of Sciences, Moscow
b Moscow State University of Geodesy and Cartography

Abstract: We consider positive integers whose number of prime divisors is congruent to $l$ modulo $k$. In this case, the calculation of prime divisors can be made either with or without taking into account the multiplicity, and the divisors themselves can be subjected to the additional requirement of belonging to some special set. We show that for $k\geqslant3$, the distribution pattern of these numbers, in dependence on the value of $l$, differs fundamentally from that in the case $k=2$, which was studied earlier.

Keywords: prime divisors, Perron's formula.

Funding Agency Grant Number
Russian Science Foundation 14-11-00433
This research was supported by a grant from the Russian Science Foundation (project no. 14-11-00433).


DOI: https://doi.org/10.4213/im8711

Full text: PDF file (574 kB)
First page: PDF file
References: PDF file   HTML file

English version:
Izvestiya: Mathematics, 2019, 83:1, 173–183

Bibliographic databases:

UDC: 511
MSC: Primary 11N25; Secondary 11N37
Received: 29.08.2017
Revised: 21.02.2018

Citation: M. E. Changa, “On integers whose number of prime divisors belongs to a given residue class”, Izv. RAN. Ser. Mat., 83:1 (2019), 192–202; Izv. Math., 83:1 (2019), 173–183

Citation in format AMSBIB
\Bibitem{Cha19}
\by M.~E.~Changa
\paper On integers whose number of prime divisors belongs to a~given residue class
\jour Izv. RAN. Ser. Mat.
\yr 2019
\vol 83
\issue 1
\pages 192--202
\mathnet{http://mi.mathnet.ru/izv8711}
\crossref{https://doi.org/10.4213/im8711}
\adsnasa{http://adsabs.harvard.edu/cgi-bin/bib_query?2019IzMat..83..173C}
\elib{http://elibrary.ru/item.asp?id=37045047}
\transl
\jour Izv. Math.
\yr 2019
\vol 83
\issue 1
\pages 173--183
\crossref{https://doi.org/10.1070/IM8711}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000459866800008}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85060147115}


Linking options:
  • http://mi.mathnet.ru/eng/izv8711
  • https://doi.org/10.4213/im8711
  • http://mi.mathnet.ru/eng/izv/v83/i1/p192

    SHARE: VKontakte.ru FaceBook Twitter Mail.ru Livejournal Memori.ru


    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles
  • Izvestiya Rossiiskoi Akademii Nauk. Seriya Matematicheskaya Izvestiya: Mathematics
    Number of views:
    This page:91
    References:15
    First page:13

     
    Contact us:
     Terms of Use  Registration  Logotypes © Steklov Mathematical Institute RAS, 2019