Download this article
Download this article For screen
For printing
Recent Issues
Volume 14, Issue 1
Volume 13, Issue 4
Volume 13, Issue 3
Volume 13, Issue 2
Volume 13, Issue 1
Volume 12, Issue 4
Volume 12, Issue 3
Volume 12, Issue 2
Volume 12, Issue 1
Volume 11, Issue 4
Volume 11, Issue 3
Volume 11, Issue 2
Volume 11, Issue 1
Volume 10, Issue 4
Volume 10, Issue 3
Volume 10, Issue 2
Volume 10, Issue 1
Volume 9, Issue 4
Volume 9, Issue 3
Volume 9, Issue 2
Volume 9, Issue 1
Volume 8, Issue 4
Volume 8, Issue 3
Volume 8, Issue 2
Volume 8, Issue 1
Older Issues
Volume 7, Issue 4
Volume 7, Issue 3
Volume 7, Issue 2
Volume 7, Issue 1
Volume 6, Issue 4
Volume 6, Issue 2-3
Volume 6, Issue 1
Volume 5, Issue 4
Volume 5, Issue 3
Volume 5, Issue 1-2
Volume 4, Issue 4
Volume 4, Issue 3
Volume 4, Issue 2
Volume 4, Issue 1
Volume 3, Issue 3-4
Volume 3, Issue 2
Volume 3, Issue 1
Volume 2, Issue 4
Volume 2, Issue 3
Volume 2, Issue 2
Volume 2, Issue 1
Volume 1, Issue 4
Volume 1, Issue 3
Volume 1, Issue 2
Volume 1, Issue 1
The Journal
About the journal
Ethics and policies
Peer-review process
 
Submission guidelines
Submission form
Editorial board
founded and published with the
scientific support and advice of
mathematicians from the
Moscow Institute of
Physics and Technology
Subscriptions
 
ISSN 2996-220X (online)
ISSN 2996-2196 (print)
Author Index
To Appear
 
Other MSP Journals
This article is available for purchase or by subscription. See below.
On logarithmic asymptotics for the number of restricted partitions in the exponential case

Murat V. Vakhitov and Dmitrii S. Minenkov
Vol. 12 (2023), No. 4, 297–309
DOI: 10.2140/moscow.2023.12.297
Abstract

Asymptotics for the logarithm of the number of restricted partitions is calculated in the case of exponential growth of the counting function. In terms of abstract number theory this problem is the inverse problem of the distribution of abstract primes, i.e., for a given counting function of abstract primes we calculate the asymptotics of abstract integers. While calculating the number of integers, only the limited number of abstract primes is considered and the constructed asymptotics is uniform with respect to this number. We consider only the leading term of logarithmic asymptotics, which is obtained using elementary estimations. The considered case includes the case of integers and primes themselves.

PDF Access Denied

We have not been able to recognize your IP address 3.17.183.187 as that of a subscriber to this journal.
Online access to the content of recent issues is by subscription, or purchase of single articles.

Please contact your institution's librarian suggesting a subscription, for example by using our journal-recom­mendation form. Or, visit our subscription page for instructions on purchasing a subscription.

You may also contact us at contact@msp.org
or by using our contact form.

Or, you may purchase this single article for USD 40.00:

Keywords
restricted partitions, abstract primes, abstract integers, counting function, asymptotics
Mathematical Subject Classification
Primary: 11P70, 11P81
Milestones
Received: 27 May 2022
Revised: 25 November 2023
Accepted: 12 December 2023
Published: 5 January 2024
Authors
Murat V. Vakhitov
Department of Mechanics and Mathematics
Lomonosov Moscow State University
Moscow
Russia		 National Research University Higher School of Economics
Moscow
Russia
Dmitrii S. Minenkov
Ishlinsky Institute for Problems in Mechanics
Moscow
Russia		 National Research University Higher School of Economics
Moscow
Russia
© 2023 MSP (Mathematical Sciences Publishers).