On the ternary Goldbach problem with primes in arithmetic progressions of a common module
نویسنده
چکیده
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.
منابع مشابه
Chen’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In Iwaniec’s unpublished notes [10], the exponent 1/10 can be improved to 3/11.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 کاملTernary Goldbach Problem for the Subsets of Primes with Positive Relative Densities
p|n(1−(p−1) −2) and A is a positive constant. Nowadays Vinogradov’s theorem has become a classical result in additive number theory. Later, using a similar method, van der Corput [2] proved that the primes contain infinitely many non-trivial 3-term arithmetic progressions (3AP). On the other hand, another classical result due to Roth [8] asserts that a set A of integers contains infinitely many...
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+...
متن کاملTernary Goldbach Problem for the Subsets of Primes with Positive Relative Density
p|n(1−(p−1) −2) and A is a positive constant. Nowadays Vinogradov’s theorem has become a classical result in additive number theory. For the proof of Vinogradov’s theorem, the reader may refer to [2, 10]. Later, with a similar method, van der Corput [1] proved that the primes contain infinitely many non-trivial 3-term arithmetic progressions (3AP). On the other hand, another classical result du...
متن کاملOn rainbow 4-term arithmetic progressions
{sl Let $[n]={1,dots, n}$ be colored in $k$ colors. A rainbow AP$(k)$ in $[n]$ is a $k$ term arithmetic progression whose elements have different colors. Conlon, Jungi'{c} and Radoiv{c}i'{c} cite{conlon} prove that there exists an equinumerous 4-coloring of $[4n]$ which is rainbow AP(4) free, when $n$ is even. Based on their construction, we show that such a coloring of $[4n]$...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2008