منابع مشابه
The ternary Goldbach problem
Leonhard Euler (1707–1783) – one of the greatest mathematicians of the eighteenth century and of all times – often corresponded with a friend of his, Christian Goldbach (1690–1764), an amateur and poly-math who lived and worked in Russia, just like Euler himself. In a letter written in June 1742, Goldbach made a conjecture – that is, an educated guess – on prime numbers: Es scheinet wenigstens,...
متن کاملChen’s Primes and Ternary Goldbach Problem
In Iwaniec’s unpublished notes [10], the exponent 1/10 can be improved to 3/11. In [6], Green and Tao say a prime p is Chen’s prime if p ∈ P 2 . On the other hand, in 1937 Vinogradov [18] solved the ternary Goldbach problem and showed that every sufficiently large odd integer can be represented as the sum of three primes. Two years later, using Vinogradov’s method, van der Corput [2] proved tha...
متن کاملThe ternary Goldbach problem with primes in positive density sets
Let P denote the set of all primes. P1, P2, P3 are three subsets of P . Let δ(Pi) (i = 1, 2, 3) denote the lower density of Pi in P , respectively. It is proved that if δ(P1) > 5/8, δ(P2) ≥ 5/8, and δ(P3) ≥ 5/8, then for every sufficiently large odd integer n, there exist pi ∈ Pi such that n = p1 + p2 + p3. The condition is the best possible.
متن کاملOn the ternary Goldbach problem with primes in arithmetic progressions of a common module
For A, ε > 0 and any sufficiently large odd n we show that for almost all k ≤ R := n 1/5−ε there exists a representation n = p 1 + p 2 + p 3 with primes p i ≡ b i mod k for almost all admissible triplets b 1 , b 2 , b 3 of reduced residues mod k.
متن کاملOn the Ternary Goldbach Problem with Primes in independent Arithmetic Progressions
We show that for every fixed A > 0 and θ > 0 there is a θ = θ(A, θ) > 0 with the following property. Let n be odd and sufficiently large, and let Q1 = Q2 := n 1/2(log n)−θ and Q3 := (log n) θ. Then for all q3 ≤ Q3, all reduced residues a3 mod q3, almost all q2 ≤ Q2, all admissible residues a2 mod q2, almost all q1 ≤ Q1 and all admissible residues a1 mod q1, there exists a representation n = p1+...
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ژورنال
عنوان ژورنال: American Journal of Mathematics
سال: 2016
ISSN: 1080-6377
DOI: 10.1353/ajm.2016.0038