On the characters of primes. I
Ю.В. Линник (1945)
Matematiceskij sbornik
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Ю.В. Линник (1945)
Matematiceskij sbornik
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Enxun Huang (2023)
Czechoslovak Mathematical Journal
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It is proved that every pair of sufficiently large odd integers can be represented by a pair of equations, each containing two squares of primes, two cubes of primes, two fourth powers of primes and 105 powers of 2.
Hongze Li (2001)
Acta Arithmetica
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Glyn Harman (2006)
Acta Arithmetica
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M. C. Liu, T. Z. Wang (2002)
Acta Arithmetica
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Gustavo Funes, Damian Gulich, Leopoldo Garavaglia, Mario Garavaglia (2008)
Visual Mathematics
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Liqun Hu, Li Yang (2017)
Open Mathematics
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In this paper, we obtained that when k = 455, every pair of large even integers satisfying some necessary conditions can be represented in the form of a pair of unlike powers of primes and k powers of 2.
Antal Balog (1985)
Banach Center Publications
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Glyn Harman, Imre Kátai (2008)
Acta Arithmetica
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Zhixin Liu, Guangshi Lü (2010)
Acta Arithmetica
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Daniel Alan Goldston, János Pintz, Cem Yalçın Yıldırım (2013)
Acta Arithmetica
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We prove that given any small but fixed η > 0, a positive proportion of all gaps between consecutive primes are smaller than η times the average gap. We show some unconditional and conditional quantitative results in this vein. In the results the dependence on η is given explicitly, providing a new quantitative way, in addition to that of the first paper in this series, of measuring the effect of the knowledge on the level of distribution of primes.
Kaisa Matomäki (2009)
Acta Arithmetica
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William D. Banks, Ahmet M. Güloğlu, C. Wesley Nevans (2007)
Acta Arithmetica
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И.М. Виноградов ([unknown])
Matematiceskij sbornik
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Jörg Brüdern, Koichi Kawada (2011)
Colloquium Mathematicae
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A new method for counting primes in a Beatty sequence is proposed, and it is shown that an asymptotic formula can be obtained for the number of such primes in a short interval.
Dieter Wolke (2005)
Acta Arithmetica
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J. Pintz, I. Z. Ruzsa (2003)
Acta Arithmetica
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