The mean behavior of primes in arithmetic progressions.
Richard H., Bays, Carter Hudson (1977)
Journal für die reine und angewandte Mathematik
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Richard H., Bays, Carter Hudson (1977)
Journal für die reine und angewandte Mathematik
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Alfred Brauer, Richard H. Hudson (1977)
Journal für die reine und angewandte Mathematik
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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.
Binbin Zhou (2009)
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.
Richard H. Hudson, Carter Bays (1983)
Journal für die reine und angewandte Mathematik
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Jan-Christoph Puchta (2003)
Acta Arithmetica
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D. A. Goldston, C. Y. Yıldırım (2001)
Acta Arithmetica
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Étienne Fouvry, Igor E. Shparlinski (2011)
Acta Arithmetica
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Yoichi Motohashi (1978)
Inventiones mathematicae
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Shanta Laishram, T. N. Shorey (2005)
Acta Arithmetica
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D.R. Heath-Brown (1982)
Journal für die reine und angewandte Mathematik
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Kaisa Matomäki (2009)
Acta Arithmetica
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Glyn Harman (2006)
Acta Arithmetica
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František Marko, Štefan Porubský (2015)
Colloquium Mathematicae
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We investigate properties of coset topologies on commutative domains with an identity, in particular, the 𝓢-coprime topologies defined by Marko and Porubský (2012) and akin to the topology defined by Furstenberg (1955) in his proof of the infinitude of rational primes. We extend results about the infinitude of prime or maximal ideals related to the Dirichlet theorem on the infinitude of primes from Knopfmacher and Porubský (1997), and correct some results from that paper. Then we determine...
N. Saradha, R. Tijdeman (2008)
Acta Arithmetica
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Roger C. Baker (2012)
Acta Arithmetica
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P.D.T.A. Elliott (1995)
Journal für die reine und angewandte Mathematik
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D.R. Heath-Brown (1988)
Journal für die reine und angewandte Mathematik
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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.