On a Goldbach-type problem for the Liouville function

Alexander P. Mangerel

On a Goldbach-type problem for the Liouville function

Number Theory 2024-05-03 v2

Authors: Alexander P. Mangerel

Abstract

Let $\lambda$ denote the Liouville function. We show that for all sufficiently large integers $N$ , the (non-trivial) convolution sum bound $\left|\sum_{1 \leq n < N} \lambda(n) \lambda(N-n)\right| < N-1$ holds. This (essentially) answers a question posed at the 2018 AIM workshop on Sarnak's conjecture.

Keywords

multiplicative functions liouville theorem divisor function

Cite

@article{arxiv.2404.12117,
  title  = {On a Goldbach-type problem for the Liouville function},
  author = {Alexander P. Mangerel},
  journal= {arXiv preprint arXiv:2404.12117},
  year   = {2024}
}

Comments

14 pages; fixed several typos and added a remark, comments welcome

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