Goldbach Representations with several primes
Thi Thu Nguyen

TL;DR
This paper extends the analysis of Goldbach representations to sums of k primes, providing an asymptotic formula with improved error terms and linking the problem to the Riemann Hypothesis.
Contribution
It generalizes previous results for two primes to any number of primes k and establishes an equivalence between the average order of representations and the Riemann Hypothesis.
Findings
Derived an asymptotic formula for k-prime Goldbach representations
Improved error terms in the asymptotic estimates
Proved the equivalence between average order and the Riemann Hypothesis
Abstract
We study an asymptotic formula for average orders of Goldbach representations of an integer as the sum of k primes. We extend the existing result for k=2 to a general k, for which we obtain a better error term. Moreover, we prove an equivalence between the Riemann Hypothesis and a good average order in this case.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsAnalytic Number Theory Research · History and advancements in chemistry · Finite Group Theory Research
