@inproceedings{Tao2007AdditiveC,
author={Terence Tao and Van H. Vu},
year={2007}
}
• Published in
2007
• Mathematics
2.4. Vinogradov’s three-primes theorem. Sound/Gowers spend some effort discussing Vinogradov’s result that all large odd integers are the sum of three primes. We will give their (and Hardy-Littlewood’s) proof, conditional on GRH. This introduces the circle method, which is a nice application of Fourier analytic techniques to additive problems. I also plan on one additional lecture on the circle method which briefly explains its other applications: Vinogradov without GRH, partitions, Waring’s…
865 Citations
AN $L$ -FUNCTION-FREE PROOF OF VINOGRADOV’S THREE PRIMES THEOREM
• X. Shao
• Mathematics
Forum of Mathematics, Sigma
• 2014
Abstract We give a new proof of Vinogradov’s three primes theorem, which asserts that all sufficiently large odd positive integers can be written as the sum of three primes. Existing proofs rely on
Plünnecke ’ s Inequality 2 . 1 Commutative graphs : definition and notation
Plünnecke’s inequality is the standard tool to obtain estimates on the cardinality of sumsets and has many applications in additive combinatorics. We present a new proof. The main novelty is that the
Bohr sets and multiplicative Diophantine approximation
• Sam Chow
• Mathematics
Duke Mathematical Journal
• 2018
In two dimensions, Gallagher's theorem is a strengthening of the Littlewood conjecture that holds for almost all pairs of real numbers. We prove an inhomogeneous fibre version of Gallagher's theorem,
Algebraic and combinatorial methods in the theory of set addition
This report contains a good part of the results of my reserach in additive combinatorics I have been conducting during the last decade, the central theme being the structural theory of set addition.
J. (2015). Finite field models in arithmetic combinatorics – ten years on. Finite Fields and Their Applications , 32 , 233-274.
• Mathematics
• 2014
. It has been close to ten years since the publication of Green’s inﬂuential survey Finite ﬁeld models in additive combinatorics [ ? ], in which the author championed the use of high-dimensional
Higher-rank Bohr sets and multiplicative diophantine approximation
• Mathematics
Compositio Mathematica
• 2019
Gallagher’s theorem is a sharpening and extension of the Littlewood conjecture that holds for almost all tuples of real numbers. We provide a fibre refinement, solving a problem posed by Beresnevich,
Affine linear sieve, expanders, and sum-product
• Mathematics
• 2010
AbstractLet $\mathcal{O}$ be an orbit in ℤn of a finitely generated subgroup Λ of GLn(ℤ) whose Zariski closure Zcl(Λ) is suitably large (e.g. isomorphic to SL2). We develop a Brun combinatorial
It is shown that there is a universal $\epsilon>0$ so that any subset of an abelian group with subtractive doubling $K$ must be polynomially related to a set with additive energy at least $\frac{1}{K^{1-\ep silon}}$.