Re: [math-fun] binary roulette wheels
Jim Propp wrote: ----- I believe there is a sense in which the Riemann zeta function on the critical line exhibits the sort of behavior Dan is looking for. If I recall correctly, for any continuous real-valued function f on any finite interval, and for any positive epsilon, there’s an interval on the critical line such that the zeta function differs from f by less than epsilon everywhere on the interval. ----- Aha, maybe I heard of something like that once, too. Googling led to this article: <https://en.wikipedia.org/wiki/Zeta_function_universality>. It is apparently a 2-dimensional approximation in the critical strip (not line), which I guess allows for more wiggle room. —Dan
fascinating. Is this because we can freely tune Taylor series coefficients as closely as we like by moving along the critical line?
On Oct 3, 2020, at 4:42 PM, Dan Asimov <dasimov@earthlink.net> wrote:
Jim Propp wrote: ----- I believe there is a sense in which the Riemann zeta function on the critical line exhibits the sort of behavior Dan is looking for. If I recall correctly, for any continuous real-valued function f on any finite interval, and for any positive epsilon, there’s an interval on the critical line such that the zeta function differs from f by less than epsilon everywhere on the interval. -----
Aha, maybe I heard of something like that once, too. Googling led to this article: <https://en.wikipedia.org/wiki/Zeta_function_universality>. It is apparently a 2-dimensional approximation in the critical strip (not line), which I guess allows for more wiggle room.
—Dan
_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://linkprotect.cudasvc.com/url?a=https%3a%2f%2fmailman.xmission.com%2fc...
Cris Moore moore@santafe.edu
participants (2)
-
Cris Moore -
Dan Asimov