关于柳维尔函数的哥德巴赫问题

Pub Date : 2024-07-03 DOI:10.1093/imrn/rnae149

Alexander P Mangerel

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引用次数: 0

摘要

让 $\lambda $ 表示柳维尔函数。我们证明，对于所有 $N \geq 11$，（非难）卷积和约束 $$ \begin{align*} & \left|\sum_{n < N}\lambda(n) \lambda(N-n)\right| < N-1 \end{align*} $$ 成立。$$ 成立。我们还确定了卷积和中不发生抵消的所有 $N$。这回答了 2018 年 AIM 研讨会上提出的一个关于萨尔纳克猜想的问题。

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On a Goldbach-Type Problem for the Liouville Function

Let $\lambda $ denote the Liouville function. We show that for all $N \geq 11$, the (non-trivial) convolution sum bound $$ \begin{align*} & \left|\sum_{n < N} \lambda(n) \lambda(N-n)\right| < N-1 \end{align*} $$ holds. We also determine all $N$ for which no cancellation in the convolution sum occurs. This answers a question posed at the 2018 AIM workshop on Sarnak’s conjecture.

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