数学平均Chowla猜想的奇数阶情形
Odd order cases of the logarithmically averaged Chowla conjecture
摘要：
Chowla的一个著名猜想指出，刘维尔函数$λ(n)$与其位移的相关性可以忽略不计。最近，作者建立了关于乘性函数相关性的代数平均Elliott猜想的一个弱形式，它包含了代数平均Chowla猜想的所有奇阶情形.本文给出了数学平均Chowla猜想奇阶情形的一个新的较短的证明。特别是，这个证明避免了所有提到的遍历论，其中有一个重要的作用，在以前的证明。
英文摘要：
A famous conjecture of Chowla states that the Liouville function $λ(n)$ has negligible correlations with its shifts. Recently, the authors established a weak form of the logarithmically averaged Elliott conjecture on correlations of multiplicative functions, which in turn implied all the odd order cases of the logarithmically averaged Chowla conjecture. In this note, we give a new and shorter proof of the odd order cases of the logarithmically averaged Chowla conjecture. In particular, this proof avoids all mention of ergodic theory, which had an important role in the previous proof.
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