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

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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 Iλ(N,h): we get Iλ(N,h)≪ NhL³+Nh²¹/²⁰, with L:= N. We also give similar results for other related arithmetic functions, like the Möbius function μ(n) (=λ(n) on square-free n).