Ternary Goldbach's Problem Involving Primes of a Special Type

TL;DR

This paper addresses a variant of the ternary Goldbach problem involving primes constrained by a quadratic irrationality, demonstrating solutions under specific fractional conditions.

Contribution

It introduces a new approach to the ternary Goldbach problem involving primes with fractional parts related to a quadratic irrationality.

Findings

Solved the ternary Goldbach problem variant for primes with fractional parts in (a,b)

Established conditions for primes involving quadratic irrationality

Extended understanding of prime distributions under fractional constraints

Abstract

Let $\eta$ be a quadratic irrationality. The variant of a ternary problem of Goldbach involving primes such that $a<\{\eta p\}<b$, where $a$ and $b$ are arbitrary numbers of the interval $(0,1)$, solved in this paper.