On cluster primes
Christian Elsholtz (2003)
Acta Arithmetica
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Christian Elsholtz (2003)
Acta Arithmetica
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Yingchun Cai, Minggao Lu (2003)
Acta Arithmetica
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Jürgen G. Hinz (1986/87)
Manuscripta mathematica
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Glyn Harman (2006)
Acta Arithmetica
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D. W. Dubois
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CONTENTSIntroduction....................................................................................... 5§ 1. Preliminaries............................................................................ 8§ 2. Constructions........................................................................... 10§ 3. Orders and modes.................................................................. 13§ 4. Conic primes............................................................................ 19§...
Yuan Wang (1978-1979)
Séminaire Delange-Pisot-Poitou. Théorie des nombres
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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).
Eleni Agathocleous (2014)
Acta Arithmetica
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The class numbers h⁺ of the real cyclotomic fields are very hard to compute. Methods based on discriminant bounds become useless as the conductor of the field grows, and methods employing Leopoldt's decomposition of the class number become hard to use when the field extension is not cyclic of prime power. This is why other methods have been developed, which approach the problem from different angles. In this paper we extend one of these methods that was designed for real cyclotomic fields...
J.F. Voloch, Arnaldo Garcia (1987)
Manuscripta mathematica
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Kaisa Matomäki (2009)
Acta Arithmetica
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Hakan Ali-John Seyalioglu (2009)
Acta Arithmetica
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Elkenbracht-Huizing, Marije (1996)
Experimental Mathematics
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Dieter Wolke (2005)
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.
Glyn Harman, Imre Kátai (2008)
Acta Arithmetica
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Yingchun Cai (2002)
Acta Arithmetica
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Gustavo Funes, Damian Gulich, Leopoldo Garavaglia, Mario Garavaglia (2008)
Visual Mathematics
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Hershy Kisilevsky, Michael O. Rubinstein (2015)
Acta Arithmetica
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We consider the problem of determining whether a set of primes, or, more generally, prime ideals in a number field, can be realized as a finite union of residue classes, or of Frobenius conjugacy classes. We give necessary conditions for a set to be realized in this manner, and show that the subset of primes consisting of every other prime cannot be expressed in this way, even if we allow a finite number of exceptions.