On the correlation between M{o}bius and polynomial phases in short arithmetic progressions


الملخص بالإنكليزية

We obtain an estimate for the average value of the product of the Mobius function and any polynomial phase over short intervals and arithmetic progressions simultaneously. As a consequence, we prove that the product of M{o}bius and any polynomial phase is disjoint from arithmetic functions realized in certain rigid dynamical systems, such as any finite products of translations of Mobius squared.

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