Primes in arithmetic progressions to spaced moduli
Roger C. Baker (2012)
Acta Arithmetica
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Roger C. Baker (2012)
Acta Arithmetica
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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.
Liangyi Zhao (2004)
Acta Arithmetica
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E. Bombieri, J.B. Friedlander, H. Iwaniec (1987)
Mathematische Annalen
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Étienne Fouvry, Igor E. Shparlinski (2011)
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.
P.D.T.A. Elliott (1995)
Journal für die reine und angewandte Mathematik
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Jan-Christoph Puchta (2003)
Acta Arithmetica
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Kaisa Matomäki (2009)
Acta Arithmetica
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Glyn Harman (2006)
Acta Arithmetica
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Antal Balog (1985)
Banach Center Publications
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E. Grosswald (1980)
Journal für die reine und angewandte Mathematik
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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.
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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Hongze Li (2001)
Acta Arithmetica
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Binbin Zhou (2009)
Acta Arithmetica
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Jan Mycielski (1989)
Colloquium Mathematicae
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Hakan Ali-John Seyalioglu (2009)
Acta Arithmetica
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