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Funktsional. Anal. i Prilozhen., 2016, Volume 50, Issue 4, Pages 55–75 (Mi faa3256)  

This article is cited in 3 scientific papers (total in 3 papers)

On the Asymptotics of the Element Counting Function in an Additive Arithmetic Semigroup with Exponential Counting Function of Prime Generators

D. S. Minenkovab, V. E. Nazaikinskiiab, V. L. Chernyshevc

a Ishlinsky Institute for Problems in Mechanics, Russian Academy of Sciences, Moscow, Russia
b Moscow Institute of Physics and Technology (State University), Dolgoprudny, Moscow Oblast, Russia
c National Research University Higher School of Economics, Moscow, Russia

Abstract: We find the asymptotics of the element counting function for an additive arithmetic semigroup with exponential growth of the counting function of prime generators.

Keywords: arithmetic semigroup, inverse abstract prime number theorem, counting function, entropy, asymptotics

Funding Agency Grant Number
Russian Science Foundation 14-11-00432
This work was supported by the Russian Science Foundation under grant 14-11-00432.


DOI: https://doi.org/10.4213/faa3256

Full text: PDF file (262 kB)
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English version:
Functional Analysis and Its Applications, 2016, 50:4, 291–307

Bibliographic databases:

UDC: 511.3
Received: 17.12.2015

Citation: D. S. Minenkov, V. E. Nazaikinskii, V. L. Chernyshev, “On the Asymptotics of the Element Counting Function in an Additive Arithmetic Semigroup with Exponential Counting Function of Prime Generators”, Funktsional. Anal. i Prilozhen., 50:4 (2016), 55–75; Funct. Anal. Appl., 50:4 (2016), 291–307

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. V. L. Chernyshev, A. A. Tolchennikov, A. I. Shafarevich, “Behavior of quasi-particles on hybrid spaces. Relations to the geometry of geodesics and to the problems of analytic number theory”, Regul. Chaotic Dyn., 21:5 (2016), 531–537  mathnet  crossref  mathscinet  zmath  isi  elib  scopus
    2. V. P. Maslov, “Negative energy, debts, and disinformation from the viewpoint of analytic number theory”, Russ. J. Math. Phys., 23:3 (2016), 355–368  crossref  mathscinet  zmath  isi  scopus
    3. D. S. Minenkov, V. E. Nazaikinskii, V. L. Chernyshev, “On the limit form of the elements of an arithmetic semigroup with exponentially growing counting functions of basis elements”, Dokl. Math., 95:3 (2017), 226–229  crossref  crossref  mathscinet  zmath  isi  elib  scopus
  • Функциональный анализ и его приложения Functional Analysis and Its Applications
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