Oilerio sandaugų analizinio pratęsimo klausimu

Santrauka

The sequence of generalized primes {v(p + kp^α)} with rational prime numbers p and v  > 1/2,  0≤ k  ≤ 1, 0 ≤ α < 1 is considered. The analicity of corresponding Euler product Z (s; v, k, α)= ∏_p (1 — (v (p + kp^α))^-s)^-1
in the domain {s : σ > α} \ (∪_ρ∪_n { s= (xβ+ iγ)/n : α < x ≤ 1} ∪ (α; 1]), where ρ = β + iγ are the zeros of Riemann zeta function, is proved.