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The primes contain arbitrarily long arithmetic progressions
 Ann. of Math
"... Abstract. We prove that there are arbitrarily long arithmetic progressions of primes. ..."
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Cited by 151 (26 self)
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Abstract. We prove that there are arbitrarily long arithmetic progressions of primes.
SOME UNSOLVED PROBLEMS
, 1957
"... ... gave occasion for an informal lecture in which I discussed various old and new questions on number theory, geometry and analysis. In the following list, I record these problems, with the addition of references and of a few further questions. ..."
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Cited by 29 (0 self)
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... gave occasion for an informal lecture in which I discussed various old and new questions on number theory, geometry and analysis. In the following list, I record these problems, with the addition of references and of a few further questions.
Mijajlović: On Kurepa problems in number theory
 Publ. Inst. Math. (N.S
, 1995
"... Dedicated to the memory of Prof.Duro Kurepa ..."
Generalising the HardyLittlewood method for primes
 In: Proceedings of the international congress of mathematicians
, 2007
"... Abstract. The HardyLittlewood method is a wellknown technique in analytic number theory. Among its spectacular applications are Vinogradov’s 1937 result that every sufficiently large odd number is a sum of three primes, and a related result of Chowla and Van der Corput giving an asymptotic for the ..."
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Cited by 5 (2 self)
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Abstract. The HardyLittlewood method is a wellknown technique in analytic number theory. Among its spectacular applications are Vinogradov’s 1937 result that every sufficiently large odd number is a sum of three primes, and a related result of Chowla and Van der Corput giving an asymptotic for the number of 3term progressions of primes, all less than N. This article surveys recent developments of the author and T. Tao, in which the HardyLittlewood method has been generalised to obtain, for example, an asymptotic for the number of 4term arithmetic progressions of primes less than N.
Arithmetic progressions and the primes  El Escorial lectures
 Collectanea Mathematica (2006), Vol. Extra., 3788 (Proceedings of the 7th International Conference on Harmonic Analysis and Partial Differential Equations, El Escorial
"... Abstract. We describe some of the machinery behind recent progress in establishing infinitely many arithmetic progressions of length k in various sets of integers, in particular in arbitrary dense subsets of the integers, and in the primes. 1. ..."
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Cited by 3 (0 self)
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Abstract. We describe some of the machinery behind recent progress in establishing infinitely many arithmetic progressions of length k in various sets of integers, in particular in arbitrary dense subsets of the integers, and in the primes. 1.
Long arithmetic progressions of primes
 Mathematics Proceedings
"... Abstract. This is an article for a general mathematical audience on the author’s work, joint with Terence Tao, establishing that there are arbitrarily long arithmetic progressions of primes. 1. introduction and history This is a description of recent work of the author and Terence Tao [11] on primes ..."
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Cited by 2 (0 self)
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Abstract. This is an article for a general mathematical audience on the author’s work, joint with Terence Tao, establishing that there are arbitrarily long arithmetic progressions of primes. 1. introduction and history This is a description of recent work of the author and Terence Tao [11] on primes in arithmetic progression. It is based on seminars given for a general mathematical
G3(N): = �
, 2002
"... We show that there exist sets of primes A, B ⊆ P ∩[1, N] with A  =s, B  =t such that all 1 2 (ai + b j) are also prime, and where s � 0.33 t N/(log N) t+1 holds, for sufficiently large N. Grosswald [4] considered the number of triples of primes in arithmetic progression: ..."
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We show that there exist sets of primes A, B ⊆ P ∩[1, N] with A  =s, B  =t such that all 1 2 (ai + b j) are also prime, and where s � 0.33 t N/(log N) t+1 holds, for sufficiently large N. Grosswald [4] considered the number of triples of primes in arithmetic progression:
A survey on additive and multiplicative decompositions of sumsets and of shifted sets
, 2009
"... In this paper we survey results on sumsets with multiplicative properties and the question if a shifted copy of a multiplicatively defined set can again be multiplicatively defined. The methods involved are of analytic nature such as the large sieve, and of combinatorial nature such as extremal gra ..."
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In this paper we survey results on sumsets with multiplicative properties and the question if a shifted copy of a multiplicatively defined set can again be multiplicatively defined. The methods involved are of analytic nature such as the large sieve, and of combinatorial nature such as extremal graph theory. 1