Timeline for answer to Proposals for polymath projects by Jack D'Aurizio

7 events

when toggle format	what		by	license	comment
Sep 20, 2017 at 11:50	comment	added	Robert Frost		Is this equivalent to convergence of $\displaystyle\frac{e^{2i}}{1}+\displaystyle\frac{e^{4i}}{2}+\displaystyle\frac{e^{8i}}{3}+\displaystyle\frac{e^{16i}}{4}+\cdots$?
Apr 13, 2017 at 12:19	history	edited	CommunityBot		replaced http://math.stackexchange.com/ with https://math.stackexchange.com/
Oct 19, 2016 at 23:39	comment	added	Vesselin Dimitrov		Right, and the problem is, little is known about the distribution of the binary digits of $\pi$. Needless to say there do exist divergent values of $g(\xi) = \sum_n \sin(2^n\xi) / n$ (while the series is convergent for Lebesgue almost all $\xi$), and so a solution to your problem would have to use special properties of the digits of $\pi$. One of course expects $\pi$ to be a normal number, but extremely little is 'known' in this direction.
Oct 19, 2016 at 23:08	comment	added	Jack D'Aurizio		@VesselinDimitrov: not according to my knowledge. That depends on the distribution of the $0,1$ digits in the binary representation of $\pi$ or $\frac{1}{\pi}$. My wild guess is that the BBP formula may provide a way to prove it.
Oct 19, 2016 at 23:06	comment	added	Vesselin Dimitrov		This should be very difficult. Do we even know, for instance, that the powers of $2$ are dense on $\mathbb{R} / 2 \pi \mathbb{Z}$?
S Oct 19, 2016 at 22:47	history	answered	Jack D'Aurizio	CC BY-SA 3.0
S Oct 19, 2016 at 22:47	history	made wiki			Post Made Community Wiki by Jack D'Aurizio