the " average restart " of a number. tommy1729 Ultimate Fellow Posts: 1,859 Threads: 402 Joined: Feb 2009 03/26/2014, 01:02 AM Let z be a nonreal complex number. z=z1 z2=exp(z1) z3=exp(z2) etc Define f(x) as f = 1 if x is within the unit circle on the complex plane ( |x| < 1 ) and 0 otherwise. Let ar_b(z) denote the " average restart " of z. "ar_b" is defined by a limit of an integer n going to +oo. ar_b(z) = lim_n [f(z1) + f(z2) + f(z3) + ... + f(zn)]/n^b = constant(z). (b > 0) What is known about this ?? regards tommy1729 « Next Oldest | Next Newest »

 Possibly Related Threads… Thread Author Replies Views Last Post [UFO] "commutative number theory " f(g) = g(f) tommy1729 0 8 03/24/2023, 11:36 PM Last Post: tommy1729 Is the Tetra-Euler Number Rational? Catullus 1 436 07/17/2022, 06:37 AM Last Post: JmsNxn Natural Properties of the Tetra-Euler Number Catullus 6 1,063 07/01/2022, 08:16 AM Last Post: Catullus Dynamical Systems and Number Theory Daniel 4 2,680 06/01/2021, 11:34 PM Last Post: JmsNxn Cellular auto : rule 30 number ? tommy1729 0 3,145 08/03/2016, 08:31 PM Last Post: tommy1729 [number theory] sieving with a_i mod p_i tommy1729 7 16,050 09/12/2014, 07:28 AM Last Post: tommy1729 [Number Theory] pi(X,x,x+2)+pi(X,x,x+4) tommy1729 1 5,001 04/11/2014, 10:33 PM Last Post: tommy1729 A conjecture about number theory and tetration tommy1729 0 3,841 10/23/2013, 09:28 PM Last Post: tommy1729 (number theory) How tommy1729 does it. tommy1729 0 3,986 08/12/2013, 09:13 PM Last Post: tommy1729 number theory EPNT : extended prime number theorem tommy1729 0 3,759 08/23/2012, 02:44 PM Last Post: tommy1729

Users browsing this thread: 1 Guest(s)