Goldbach's Problem in short intervals for numbers with a missing digit

TL;DR

This paper demonstrates that under certain assumptions about Dirichlet L-functions, most even numbers with a missing digit in short intervals are sums of two primes, advancing understanding of Goldbach's problem.

Contribution

It establishes that almost all such even integers in short intervals are Goldbach numbers assuming a zero-free region for Dirichlet L-functions.

Findings

Almost all even integers with a missing digit in short intervals are Goldbach numbers.

Results depend on assuming a zero-free region for Dirichlet L-functions.

Advances Goldbach's conjecture in specific digit-restricted contexts.

Abstract

In this paper, by assuming a zero-free region for Dirichlet L-functions, we show that almost all even integers $n$ in a short interval $[x,x+x^{2/3+\varepsilon}]$ with a missing digit are Goldbach numbers.