On the upper bound for π₂(x)
Yingchun Cai, Minggao Lu (2003)
Acta Arithmetica
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Yingchun Cai, Minggao Lu (2003)
Acta Arithmetica
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Glyn Harman (2006)
Acta Arithmetica
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Kaisa Matomäki (2009)
Acta Arithmetica
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Roger C. Baker, Liangyi Zhao (2016)
Acta Arithmetica
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We study the gaps between primes in Beatty sequences following the methods in the recent breakthrough by Maynard (2015).
Gustavo Funes, Damian Gulich, Leopoldo Garavaglia, Mario Garavaglia (2008)
Visual Mathematics
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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.
Glyn Harman, Imre Kátai (2008)
Acta Arithmetica
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Dieter Wolke (2005)
Acta Arithmetica
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Christian Elsholtz (2003)
Acta Arithmetica
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Hongze Li (2003)
Acta Arithmetica
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Henryk Iwaniec (1980)
Acta Arithmetica
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Ilaria Del Corso, Roberto Dvornicich, Denis Simon (2005)
Acta Arithmetica
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Jan Mycielski (1989)
Colloquium Mathematicae
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Zhixin Liu, Guangshi Lü (2010)
Acta Arithmetica
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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.
Antal Balog (1985)
Banach Center Publications
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P.D.T.A. Elliott (1995)
Journal für die reine und angewandte Mathematik
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