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An Averaged Chowla and Elliott Conjecture Along Independent Polynomials

An Averaged Chowla and Elliott Conjecture Along Independent Polynomials

We generalize a result of Matomäki, Radziwiłł, and Tao, by proving an averaged version of a conjecture of Chowla and a conjecture of Elliott regarding correlations of the Liouville function, or more general bounded multiplicative functions, with shifts given by independent polynomials in several variables. A new feature is that …