A Hybrid of Theorems of Goldbach and Piatetski-Shapiro*

Abstract

It is proved that for almost all sufficiently large even integers n, the prime variable equation n = p ₁ + p ₂, p ₁ ∈ P _γ is solvable, with 13=15 < γ ≤ 1, where P _γ = {p ∣ $p = {\left[ {m^{{\frac{1}{\gamma }}} } \right]}$; for integer m and prime p} is the set of the Piatetski-Shapiro primes.

Keywords

Circle method / Sieve method / Goldbach problem / 1P32 / 11P55

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