Primes with preassigned digits II
Glyn Harman, Imre Kátai (2008)
Acta Arithmetica
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Glyn Harman, Imre Kátai (2008)
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).
Li-Xia Dai, Yong-Gao Chen (2006)
Acta Arithmetica
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Noe, Tony D., Vos Post, Jonathan (2005)
Journal of Integer Sequences [electronic only]
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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.
John H. Hodges (1988)
Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni
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In 1972 the author used a result of K.F. Roth on irregularities in distribution of sequences of real numbers to prove an analogous result related to the distribution of sequences of integers in prescribed residue classes. Here, a 1972 result of W.M. Schmidt, which is an improvement of Roth's result, is used to obtain an improved result for sequences of integers.
John H. Hodges (1988)
Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti
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In 1972 the author used a result of K.F. Roth on irregularities in distribution of sequences of real numbers to prove an analogous result related to the distribution of sequences of integers in prescribed residue classes. Here, a 1972 result of W.M. Schmidt, which is an improvement of Roth's result, is used to obtain an improved result for sequences of integers.
M. Wunderlich (1969)
Acta Arithmetica
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Glyn Harman (2006)
Acta Arithmetica
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R.C. Baker, G. Harman (1996)
Mathematische Zeitschrift
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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.
Alex Kontorovich (2014)
Annales de la faculté des sciences de Toulouse Mathématiques
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We discuss the notion of a “Level of Distribution” in two settings. The first deals with primes in progressions, and the role this plays in Yitang Zhang’s theorem on bounded gaps between primes. The second concerns the Affine Sieve and its applications.
Dieter Wolke (2005)
Acta Arithmetica
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Gustavo Funes, Damian Gulich, Leopoldo Garavaglia, Mario Garavaglia (2008)
Visual Mathematics
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Kaisa Matomäki (2009)
Acta Arithmetica
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Chaumont, Alain, Müller, Tom (2006)
Journal of Integer Sequences [electronic only]
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Alfred Rényi (1951)
Compositio Mathematica
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