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

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Funktsional'nyi Analiz i ego Prilozheniya, 2016, Volume 50, Issue 4, Pages 55–75
DOI: https://doi.org/10.4213/faa3256 (Mi faa3256)

This article is cited in 8 scientific papers (total in 8 papers)

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

D. S. Minenkov^ab, V. E. Nazaikinskii^ab, V. L. Chernyshev^c

^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

Full-text PDF (262 kB) Citations (8)

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

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.

Received: 17.12.2015

English version:
Functional Analysis and Its Applications, 2016, Volume 50, Issue 4, Pages 291–307
DOI: https://doi.org/10.1007/s10688-016-0160-1

Bibliographic databases:

Document Type: Article

UDC: 511.3

Language: Russian

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

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This publication is cited in the following 8 articles:

Murat V. Vakhitov, Dmitrii S. Minenkov, “On logarithmic asymptotics for the number of restricted partitions in the exponential case”, Moscow J. Comb. Number Th., 12:4 (2023), 297
D. S. Minenkov, V. E. Nazaikinskii, T. W. Hilberdink, V. L. Chernyshev, “Restricted partions: the polynomial case”, Funct. Anal. Appl., 56:4 (2022), 299–309
V. L. Chernyshev, T. W. Hilberdink, V. E. Nazaikinskii, “Asymptotics of the number of restricted partitions”, Russ. J. Math. Phys., 27:4 (2020), 456–468
V. L. Chernyshev, D. S. Minenkov, V. E. Nazaikinskii, “Typical Shape of Elements in an Arithmetical Semigroup with Exponentially Growing Prime Counting Function and Deviations from the Bose–Einstein Distribution”, Math. Notes, 104:6 (2018), 939–942
Andrei Shafarevich, Springer Proceedings in Mathematics & Statistics, 273, Recent Developments in Integrable Systems and Related Topics of Mathematical Physics, 2018, 183
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
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
V. P. Maslov, “Negative energy, debts, and disinformation from the viewpoint of analytic number theory”, Russ. J. Math. Phys., 23:3 (2016), 355–368

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

Functional Analysis and Its Applications

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