Timeline for What is known about $\sum_{n \leq x} \mu(n) \varphi(n)$?

8 events

when toggle format	what		by	license	comment
Dec 17, 2015 at 19:13	history	edited	Greg Martin	CC BY-SA 3.0	added 175 characters in body
Dec 17, 2015 at 11:05	vote	accept	Jeffrey Shallit
Dec 17, 2015 at 7:16	comment	added	Denis Chaperon de Lauzières		To get the (Z_{gamma}) independent, one probably also needs to assume linear independance of ordinates of zeros of zeta...
Dec 17, 2015 at 6:49	history	edited	Greg Martin	CC BY-SA 3.0	added 21 characters in body
Dec 17, 2015 at 2:51	comment	added	Lucia		You might need to change your explicit formula a bit -- there'll be $1/\zeta^{\prime}(\rho)$'s in the denominator. So like with the usual partial sums of the Mobius function, this would be a bit more painful to work with than the analogs for $\psi(x)$.
Dec 17, 2015 at 2:36	comment	added	Peter Humphries		See chapter 15 of Montgomery and Vaughan's book; the methods there produce sign changes for $\psi(x)$, and the same methods would show that $f(x)/x^{3/2}$ changes sign infinitely often.
Dec 16, 2015 at 23:04	comment	added	Jeffrey Shallit		Great! But what can be proved, if anything, unconditionally?
Dec 16, 2015 at 22:12	history	answered	Greg Martin	CC BY-SA 3.0