References & Citations
Mathematics > Number Theory
Title: On a Goldbach-type problem for the Liouville function
(Submitted on 18 Apr 2024 (v1), last revised 2 May 2024 (this version, v2))
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.
Submission history
From: Alexander Mangerel [view email][v1] Thu, 18 Apr 2024 12:10:01 GMT (19kb)
[v2] Thu, 2 May 2024 14:48:54 GMT (19kb)
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