The ternary Goldbach conjecture with primes in thin subsets

摘要

First, we construct a thin subset S of primes, satisfying vertical bar S boolean AND[1,x]vertical bar x(26/29+epsilon) such that every sufficiently large odd integer N can be represented as [GRAPHICS] Second, let k be a prime number and bj positive integers with (b(j), k)=1, j=1,2,3. We show that, for any F > 0, and for all but O(R(log R) (- F)) prime moduli k <= R = N(9/58) - epsilon, every sufficiently large odd integer N=b(1)+b(2)+b(3) (mod k) can be written as [GRAPHICS]