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Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2021, Volume 314, Pages 152–210
DOI: https://doi.org/10.4213/tm4163 (Mi tm4163) 		 
This article is cited in 2 scientific papers (total in 2 papers)

Consecutive Primes in Short Intervals

Artyom O. Radomskii

Steklov Mathematical Institute of Russian Academy of Sciences, ul. Gubkina 8, Moscow, 119991 Russia
Full-text PDF (486 kB) Citations (2)
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DOI: https://doi.org/10.4213/tm4163
Abstract: We obtain a lower bound for $\#\{x/2<p_n\leq x:\, p_n\equiv \dots \equiv p_{n+m}\equiv a\pmod {q}$, $p_{n+m} - p_n\leq y\}$, where $p_n$ is the $n$th prime.
Keywords: Euler's totient function, sieve methods, distribution of prime numbers.
Funding agency Grant number
Ministry of Science and Higher Education of the Russian Federation 075-15-2019-1614
This work was performed at the Steklov International Mathematical Center and supported by the Ministry of Science and Higher Education of the Russian Federation (agreement no. 075-15-2019-1614).
Received: July 1, 2020
Revised: October 28, 2020
Accepted: November 3, 2020
English version:
Proceedings of the Steklov Institute of Mathematics, 2021, Volume 314, Pages 144–202
DOI: https://doi.org/10.1134/S008154382104009X
Bibliographic databases:
Document Type: Article
UDC: 511.33
Language: Russian
Citation: Artyom O. Radomskii, “Consecutive Primes in Short Intervals”, Analytic and Combinatorial Number Theory, Collected papers. In commemoration of the 130th birth anniversary of Academician Ivan Matveevich Vinogradov, Trudy Mat. Inst. Steklova, 314, Steklov Math. Inst., Moscow, 2021, 152–210; Proc. Steklov Inst. Math., 314 (2021), 144–202
Citation in format AMSBIB
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    • This publication is cited in the following 2 articles:
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    		Труды Математического института имени В. А. Стеклова Proceedings of the Steklov Institute of Mathematics
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