Primes in arithmetic progressions
Etienne Fouvry, Henryk Iwaniec (1983)
Acta Arithmetica
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Etienne Fouvry, Henryk Iwaniec (1983)
Acta Arithmetica
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Heini Halberstam (1971-1972)
Séminaire Delange-Pisot-Poitou. Théorie des nombres
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Binbin Zhou (2009)
Acta Arithmetica
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Charles E. Chace (1992)
Acta Arithmetica
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David Rodney (Roger) Heath-Brown (1985)
Revista Matemática Iberoamericana
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The object of this paper is to present new proofs of the classical ternary theorems of additive prime number theory. Of these the best known is Vinogradov's result on the representation of odd numbers as the sums of three primes; other results will be discussed later. Earlier treatments of these problems used the Hardy-Littlewood circle method, and are highly analytical. In contrast, the method we use here is a (technically) elementary deduction from the Siegel-Walfisz Prime Number Theory....
Étienne Fouvry, Igor E. Shparlinski (2011)
Acta Arithmetica
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D. A. Goldston, C. Y. Yıldırım (2001)
Acta Arithmetica
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R. Vaughan (1980)
Acta Arithmetica
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Shanta Laishram, T. N. Shorey (2005)
Acta Arithmetica
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Hamel, Mariah, Łaba, Izabella (2008)
Integers
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N. Saradha, R. Tijdeman (2008)
Acta Arithmetica
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E. Grosswald (1980)
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.