Density ternary Goldbach for primes in a fixed residue class

Key Points

• Every sufficiently large odd integer can be expressed as a sum of three primes from a dense subset.
• If the relative density of primes is above 50%, it ensures representability for certain integers.
• The threshold for relative density is shown to be optimal in this context, confirming previous conjectures.
• This work builds on Goldbach's conjecture in a specific prime residue class, providing new insights.