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Primes of the form $[{n}^c]$ with square-free $n$

UDC 621 Let $[\, \cdot\,]$ be the floor function. We show that if $1<c<\dfrac{3849}{3334},$ then there exist infinitely many prime numbers of the form $[n^c],$ where $n$ is square-free.

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Дата:2024
Автор: Dimitrov, S. I.
Формат: Стаття
Мова:Англійська
Опубліковано: Institute of Mathematics, NAS of Ukraine 2024
Онлайн доступ:https://umj.imath.kiev.ua/index.php/umj/article/view/7258
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Назва журналу:Ukrains’kyi Matematychnyi Zhurnal
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Ukrains’kyi Matematychnyi Zhurnal
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author Dimitrov, S. I.
Dimitrov, S. I.
author_facet Dimitrov, S. I.
Dimitrov, S. I.
author_sort Dimitrov, S. I.
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datestamp_date 2024-06-19T00:35:10Z
description UDC 621 Let $[\, \cdot\,]$ be the floor function. We show that if $1<c<\dfrac{3849}{3334},$ then there exist infinitely many prime numbers of the form $[n^c],$ where $n$ is square-free.
doi_str_mv 10.3842/umzh.v76i2.7258
first_indexed 2026-03-24T03:32:06Z
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fulltext Skip to main content Log in Menu Find a journal Publish with us Track your research Search Saved research Cart Home Ukrainian Mathematical Journal Article Primes of the form [nc] with Square-Free n Published: 17 August 2024 Volume 76, pages 243–253, (2024) Cite this article Save article View saved research Ukrainian Mathematical Journal Aims and scope Submit manuscript S. I. Dimitrov1  34 Accesses 1 Citation Explore all metrics Let [·] be the floor function. We show that if 1 < c < \(\frac{3849}{3334}\), then there exist infinitely many prime numbers of the form [nc], where n is square free. This is a preview of subscription content, log in via an institution to check access. Access this article Log in via an institution Subscribe and save Springer+ from €37.37 /Month Starting from 10 chapters or articles per month Access and download chapters and articles from more than 300k books and 2,500 journals Cancel anytime View plans Buy Now Buy article PDF 39,95 € Price includes VAT (Ukraine) Instant access to the full article PDF. Institutional subscriptions Similar content being viewed by others Representing Positive Integers as a Sum of a Squarefree Number and a Small Prime Chapter © 2025 A diophantine equation involving special prime numbers Article 20 October 2022 On a Logarithmic Equation by Primes Chapter © 2022 Explore related subjects Discover the latest articles, books and news in related subjects, suggested using machine learning. Combinatorics Computational Number Theory Mathematics Number Theory Real Functions Special Functions Additive and Multiplicative Properties of Prime Numbers References R. C. Baker, “The square-free divisor problem,” Quart. J. Math. Oxford Ser. (2), 45, 269–277 (1994). Article  MathSciNet  Google Scholar  R. C. Baker, G. Harman, and J. Rivat, “Primes of the form [nc],” J. Number Theory, 50, 261–277 (1995). Article  MathSciNet  Google Scholar  R. C. Baker,W. Banks, V. Guo, and A. Yeager, “Piatetski-Shapiro primes from almost primes,” Monatsh. Math., 174, 357–370 (2014). Article  MathSciNet  Google Scholar  W. D. Banks, V. Guo, and I. Shparlinski, “Almost primes of the form [pc],” Indag. Math., 27, 423–436 (2016). Article  MathSciNet  Google Scholar  S. W. Graham and G. Kolesnik, Van der Corput’s Method of Exponential Sums, Cambridge Univ. Press, New York (1991). Book  Google Scholar  D. R. Heath-Brown, “Prime numbers in short intervals and a generalized Vaughan identity,” Canad. J. Math., 34, 1365–1377 (1982). Article  MathSciNet  Google Scholar  D. R. Heath-Brown, “The Piatetski-Shapiro prime number theorem,” J. Number Theory, 16, 242–266 (1983). Article  MathSciNet  Google Scholar  C. H. Jia, “On Piatetski-Shapiro prime number theorem II,” Sci. China, Ser. A, 36, 913–926 (1993). C. H. Jia, “On Piatetski-Shapiro prime number theorem,” Chinese Ann. Math., Ser. A, 15, 9–22 (1994). G. A. Kolesnik, “The distribution of primes in sequences of the form [nc],” Mat. Zametki, 2, 117–128 (1967). MathSciNet  Google Scholar  G. A. Kolesnik, “Primes of the form [nc],” Pacific J. Math., 118, 437–447 (1985). Article  MathSciNet  Google Scholar  A. Kumchev, “On the distribution of prime numbers of the form [nc],” Glasgow Math. J., 41, 85–102 (1999). Article  MathSciNet  Google Scholar  D. Leitmann, “Abschatzung trigonometrischer Summen,” J. Reine Angew. Math., 317, 209 –219 (1980). MathSciNet  Google Scholar  H. Q. Liu and J. Rivat, “On the Piatetski-Shapiro prime number theorem,” Bull. London Math. Soc., 24, 143–147 (1992). Article  MathSciNet  Google Scholar  I. I. Piatetski-Shapiro, “On the distribution of prime numbers in sequences of the form [f(n)],” Mat. Sb., 33, 559–566 (1953). MathSciNet  Google Scholar  J. Rivat, Autour d’Un Theorem de Piatetski-Shapiro, Thesis, Université de Paris Sud (1992). Google Scholar  J. Rivat and P. Sargos, “Nombres premiers de la forme [nc],” Canad. J. Math., 53, 414–433 (2001). Article  MathSciNet  Google Scholar  J. Rivat and J. Wu, “Prime numbers of the form [nc],” Glasgow Math. J., 43, 237–254 (2001). Article  MathSciNet  Google Scholar  O. Robert and P. Sargos, “Three-dimensional exponential sums with monomials,” J. Reine Angew. Math., 591, 1–20 (2006). Article  MathSciNet  Google Scholar  J. D. Vaaler, “Some extremal functions in Fourier analysis,” Bull. Amer. Math. Soc. (N.S.), 12, 183–216 (1985). Download references Author information Authors and Affiliations Faculty of Applied Mathematics and Informatics, Technical University of Sofia, Sofia, Bulgaria S. I. Dimitrov Authors S. I. DimitrovView author publications Search author on:PubMed Google Scholar Corresponding author Correspondence to S. I. Dimitrov. Additional information Published in Ukrains’kyi Matematychnyi Zhurnal, Vol. 76, No. 2, pp. 224–233, February, 2024. Ukrainian DOI: https://doi.org/10.3842/umzh.v76i2.7258. Rights and permissions Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law. Reprints and permissions About this article Cite this article Dimitrov, S.I. Primes of the form [nc] with Square-Free n. Ukr Math J 76, 243–253 (2024). https://doi.org/10.1007/s11253-024-02318-7 Download citation Received: 12 July 2022 Published: 17 August 2024 Version of record: 17 August 2024 Issue date: July 2024 DOI: https://doi.org/10.1007/s11253-024-02318-7 Share this article Anyone you share the following link with will be able to read this content: Get shareable linkSorry, a shareable link is not currently available for this article. Copy shareable link to clipboard Provided by the Springer Nature SharedIt content-sharing initiative Access this article Log in via an institution Subscribe and save Springer+ from €37.37 /Month Starting from 10 chapters or articles per month Access and download chapters and articles from more than 300k books and 2,500 journals Cancel anytime View plans Buy Now Buy article PDF 39,95 € Price includes VAT (Ukraine) Instant access to the full article PDF. 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spelling umjimathkievua-article-72582024-06-19T00:35:10Z Primes of the form $[{n}^c]$ with square-free $n$ Primes of the form $[{n}^c]$ with square-free $n$ Dimitrov, S. I. Dimitrov, S. I. Prime numbers $\cdot$ Square-free numbers $\cdot$ Exponential sums UDC 621 Let $[\, \cdot\,]$ be the floor function.&amp;nbsp;We show that if $1&amp;lt;c&amp;lt;\dfrac{3849}{3334},$ then there exist infinitely many prime numbers of the form&amp;nbsp;$[n^c],$ where $n$ is square-free. УДК 621 Прості числа вигляду $[{n}^c]$,&amp;nbsp; де $n$ не є&amp;nbsp;квадратом Нехай $[\, \cdot\,]$ – ціла частина числа.&amp;nbsp;Показано, що для $1&amp;lt;c&amp;lt;\dfrac{3849}{3334}$&amp;nbsp; існує нескінченно багато простих чисел вигляду $[n^c],$ де $n$ не є квадратом. Institute of Mathematics, NAS of Ukraine 2024-02-28 Article Article application/pdf https://umj.imath.kiev.ua/index.php/umj/article/view/7258 10.3842/umzh.v76i2.7258 Ukrains’kyi Matematychnyi Zhurnal; Vol. 76 No. 2 (2024); 224-233 Український математичний журнал; Том 76 № 2 (2024); 224-233 1027-3190 en https://umj.imath.kiev.ua/index.php/umj/article/view/7258/9726 Copyright (c) 2024 Stoyan Dimitrov
spellingShingle Dimitrov, S. I.
Dimitrov, S. I.
Primes of the form $[{n}^c]$ with square-free $n$
title Primes of the form $[{n}^c]$ with square-free $n$
title_alt Primes of the form $[{n}^c]$ with square-free $n$
title_full Primes of the form $[{n}^c]$ with square-free $n$
title_fullStr Primes of the form $[{n}^c]$ with square-free $n$
title_full_unstemmed Primes of the form $[{n}^c]$ with square-free $n$
title_short Primes of the form $[{n}^c]$ with square-free $n$
title_sort primes of the form $[{n}^c]$ with square-free $n$
topic_facet Prime numbers $\cdot$ Square-free numbers $\cdot$ Exponential sums
url https://umj.imath.kiev.ua/index.php/umj/article/view/7258
work_keys_str_mv AT dimitrovsi primesoftheformncwithsquarefreen
AT dimitrovsi primesoftheformncwithsquarefreen

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