On the symmetry of the Liouville function in almost all short intervals

Giovanni Coppola

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arXiv · 1103.4451

On the symmetry of the Liouville function in almost all short intervals

Giovanni Coppola

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Abstract

We prove a kind of "almost all symmetry" result for the Liouville function $λ(n):=(-1)^{Ω(n)}$, giving non-trivial bounds for its "symmetry integral", say $I_λ(N,h)$ : we get $I_λ(N,h)\ll NhL^3+Nh^{21/20}$, with $L:=\log N$. We also give similar results for other related arithmetic functions, like the Möbius function $μ(n)$ ($=λ(n)$ on square-free $n$).

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Giovanni Coppola. 2011-05-23. On the symmetry of the Liouville function in almost all short intervals. https://arxiv.org/abs/1103.4451

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