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arXiv · 2404.12117

On a Goldbach-type problem for the Liouville function

Alexander P. Mangerel
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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.

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Alexander P. Mangerel. 2024-04-18. On a Goldbach-type problem for the Liouville function. https://arxiv.org/abs/2404.12117

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