On the sum of a prime and the kth power of a prime
The binary Goldbach conjecture with primes in arithmetic progressions with large modulus
It is proved that for almost all prime numbers , any fixed integer b₂, (b₂,k) = 1, and almost all integers b₁, 1 ≤ b₁ ≤ k, (b₁,k) = 1, almost all integers n satisfying n ≡ b₁ + b₂ (mod k) can be written as the sum of two primes p₁ and p₂ satisfying , i = 1,2. For the proof of this result, new estimates for exponential sums over primes in arithmetic progressions are derived.
On the difference of the consecutive primitive roots
The least primitive root in number fields
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