Primes with preassigned digits
Glyn Harman (2006)
Acta Arithmetica
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Glyn Harman (2006)
Acta Arithmetica
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Gustavo Funes, Damian Gulich, Leopoldo Garavaglia, Mario Garavaglia (2008)
Visual Mathematics
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Glyn Harman, Imre Kátai (2008)
Acta Arithmetica
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Yingchun Cai, Minggao Lu (2003)
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.
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.
Hakan Ali-John Seyalioglu (2009)
Acta Arithmetica
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Dieter Wolke (2005)
Acta Arithmetica
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Étienne Fouvry, Igor E. Shparlinski (2011)
Acta Arithmetica
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Robert J. Lemke Oliver (2012)
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).
Jan Mycielski (1989)
Colloquium Mathematicae
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Christian Elsholtz (2003)
Acta Arithmetica
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Křížek, Michal, Luca, Florian, Shparlinski, Igor E., Somer, Lawrence (2011)
Journal of Integer Sequences [electronic only]
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Chaumont, Alain, Müller, Tom (2006)
Journal of Integer Sequences [electronic only]
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Deniz A. Kaptan (2016)
Acta Arithmetica
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We implement the Maynard-Tao method of detecting primes in tuples to investigate small gaps between primes in arithmetic progressions, with bounds that are uniform over a range of moduli.
Jan-Christoph Puchta (2003)
Acta Arithmetica
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