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The Hardy–Littlewood method: Bibliography
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The article was published on 1997-01-01. It has received 109 citations till now. The article focuses on the topics: Bibliography.read more
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Elementary Methods in Number Theory
TL;DR: Nathanson as mentioned in this paper gave a first course in number theory for students with no previous knowledge of the subject, which included divisibility, prime numbers, and congruences.
Journal ArticleDOI
The cubic case of the main conjecture in Vinogradov's mean value theorem
TL;DR: In this article, a variant of the multigrade efficient congruencing method was applied to estimate Vinogradov's integral of degree 3 for moments of order 2 s, establishing strongly diagonal behaviour for 1 ⩽ s ⌽ 6.
Journal ArticleDOI
Rational solutions of certain equations involving norms
TL;DR: In this paper, the Brauer Manin obstruction was shown to be the only obstruction to the Hasse principle and weak approximation on any smooth projective model of the affine variety (Colliot-Th~l~ne and Sansuc [CSanl]).
Posted Content
Restriction theory of the Selberg sieve, with applications
Ben Green,Terence Tao +1 more
TL;DR: In this article, the Selberg sieve provides majorants for certain arithmetic sequences, such as the primes and the twin primes, and they prove an L^2-L^p restriction theorem for majorants of this type.
Journal ArticleDOI
On exponential sums over primes and application in Waring-Goldbach problem
TL;DR: In this article, it was shown that with at most O(N 7/8+e) exceptions, all positive integers up to N satisfying some necessary congruence conditions are the sum of three squares of primes.
References
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Book
Elementary Methods in Number Theory
TL;DR: Nathanson as mentioned in this paper gave a first course in number theory for students with no previous knowledge of the subject, which included divisibility, prime numbers, and congruences.
Journal ArticleDOI
The cubic case of the main conjecture in Vinogradov's mean value theorem
TL;DR: In this article, a variant of the multigrade efficient congruencing method was applied to estimate Vinogradov's integral of degree 3 for moments of order 2 s, establishing strongly diagonal behaviour for 1 ⩽ s ⌽ 6.
Journal ArticleDOI
Restriction theory of the Selberg sieve, with applications
Ben Green,Terence Tao +1 more
TL;DR: In this article, Chen et al. demontrons un theoreme de restriction L 2 -L P for the majorants of suites arithmiques with k-uplets premiers.
Journal ArticleDOI
Rational solutions of certain equations involving norms
TL;DR: In this paper, the Brauer Manin obstruction was shown to be the only obstruction to the Hasse principle and weak approximation on any smooth projective model of the affine variety (Colliot-Th~l~ne and Sansuc [CSanl]).
Journal ArticleDOI
Strichartz estimates for Schrödinger equations on irrational tori
TL;DR: In this article, the authors proved new Strichartz estimates for linear Schrodinger equations posed on d-dimensional irrational tori, and then used these estimates to prove subcritical and critical local well-posedness results for nonlinear Schrodings on irrational torians.