- Tytuł:
- The ternary Goldbach problem in arithmetic progressions
- Autorzy:
-
Liu, Jianya
Zhan, Tao - Powiązania:
- https://bibliotekanauki.pl/articles/1390842.pdf
- Data publikacji:
- 1997
- Wydawca:
- Polska Akademia Nauk. Instytut Matematyczny PAN
- Tematy:
-
ternary Goldbach problem
exponential sum over primes in arithmetic progressions
mean-value theorem - Opis:
- For a large odd integer N and a positive integer r, define b = (b₁,b₂,b₃) and $(N,r) = {b∈ ℕ³ : 1 ≤ b_j ≤ r, (b_j, r) = 1$ and b₁+b₂+b₃ ≡ N (mod r)}. It is known that $#(N,r) = r² ∏_{p|r}_{p|N} ((p-1)(p-2)/p²) ∏_{p|r}_{p∤N} ((p²-3p+3)/p²)$. Let ε > 0 be arbitrary and $R = N^{1/8-ε}$. We prove that for all positive integers r ≤ R, with at most $O(Rlog^{-A}N)$ exceptions, the Diophantine equation N = p₁+p₂+p₃, ⎨ $p_j ≡ b_j (mod r),$ j = 1,2,3,$ ⎩ with prime variables is solvable whenever b ∈ (N,r), where A > 0 is arbitrary.
- Źródło:
-
Acta Arithmetica; 1997, 82, 3; 197-227
0065-1036 - Pojawia się w:
- Acta Arithmetica
- Dostawca treści:
- Biblioteka Nauki
Artykuł