The Chen primes contain arbitrarily long arithmetic progressions
Binbin Zhou (2009)
Acta Arithmetica
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Binbin Zhou (2009)
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.
Ilwoo Cho (2017)
Special Matrices
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In this paper, we study matrices induced by arithmetic functions under certain Krein-space representations induced by (multi-)primes less than or equal to fixed positive real numbers.
N. Saradha, R. Tijdeman (2008)
Acta Arithmetica
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Yahya Ould Hamidoune, Alain Plagne (2002)
Acta Arithmetica
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Yoichi Motohashi (1978)
Inventiones mathematicae
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Jan-Christoph Puchta (2003)
Acta Arithmetica
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Yong-Gao Chen (2005)
Acta Arithmetica
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E. Grosswald (1980)
Journal für die reine und angewandte Mathematik
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(2009)
Acta Arithmetica
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Shanta Laishram, T. N. Shorey (2005)
Acta Arithmetica
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Bin Feng (2019)
Czechoslovak Mathematical Journal
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We find, via the Selberg-Delange method, an asymptotic formula for the mean of arithmetic functions on certain APs. It generalizes a result due to Cui and Wu (2014).
Tomasz Schoen (2011)
Acta Arithmetica
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Brahmagupta
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Augustus DeMorgan
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Régis de la Bretèche, Kevin Ford, Joseph Vandehey (2013)
Acta Arithmetica
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We improve known bounds for the maximum number of pairwise disjoint arithmetic progressions using distinct moduli less than x. We close the gap between upper and lower bounds even further under the assumption of a conjecture from combinatorics about Δ-systems (also known as sunflowers).
Florian Luca, Anirban Mukhopadhyay, Kotyada Srinivas (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.