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Nov 18, 2013 at 19:52 comment added Russ Woodroofe I'll comment that for the special case of the identity polynomial, this is the Mertens function. See en.wikipedia.org/wiki/Mertens_function .
Nov 18, 2013 at 15:44 comment added David E Speyer That would be my guess, but I'm not a number-theorist, just someone who reads blogs by number theorists.
Nov 18, 2013 at 15:25 comment added Seva I thus understand that no non-trivial estimates are known for sums of the form $\sum_{n\le x} \mu(P(n))$, where $P$ is a polynomial of degree ${\rm deg}(P)\ge2$?
Nov 18, 2013 at 14:51 history answered David E Speyer CC BY-SA 3.0