" fake ring theory " tommy1729 Ultimate Fellow Posts: 1,924 Threads: 415 Joined: Feb 2009 06/11/2014, 11:29 PM (This post was last modified: 06/11/2014, 11:31 PM by tommy1729.) Ok so this might be a strange title. Its the idea to combine fake function theory with ring theory. I discussed this today with my friend mick. Consider reduced real polynomial rings like F(X) := R[X]/(G(X)). Now we can define the exp for every element z of that ring by simply using the Taylor series of exp(z) mod(G(X)). Since exp(z) is entire that works fine. Now come the key ideas : exp(X) mod (G(X)) must be a polynomial in X ! Call that P(X). Now from fake function theory : exp^[1/2] is also " entire ". And then " fake function theory " gives the approximate equality : exp^[1/2](X) ~ P^[1/2](X). Depending on the degree of G , the selection of z ( Here it was z = X ) , the type of ring etc etc, we can go many directions with this idea. Multisection theory for instance. Asymptotic analysis , Galois theory , ... And it can even be used for other function than exp. Now ring elements can be linked to complex numbers , real numbers , matrices etc. To end with style : A > 0 exp^[A](X) ~ P^[A](X). Notice many rings do not have log so A > 0 is necc. regards tommy1729 « Next Oldest | Next Newest »

 Possibly Related Threads… Thread Author Replies Views Last Post [UFO] "commutative number theory " f(g) = g(f) tommy1729 0 281 03/24/2023, 11:36 PM Last Post: tommy1729 geometric function theory ideas tommy1729 0 426 12/31/2022, 12:19 AM Last Post: tommy1729 Revitalizing an old idea : estimated fake sexp'(x) = F3(x) tommy1729 0 900 02/27/2022, 10:17 PM Last Post: tommy1729 " x-theory " tommy1729 1 1,544 08/12/2021, 12:17 AM Last Post: tommy1729 Dynamical Systems and Number Theory Daniel 4 3,466 06/01/2021, 11:34 PM Last Post: JmsNxn Set theory debate : cantor 1st / Virgil argument. tommy1729 1 5,013 12/08/2015, 11:14 PM Last Post: tommy1729 [2015] Spiderweb theory tommy1729 0 4,069 03/29/2015, 06:25 PM Last Post: tommy1729 About the fake abs : f(x) = f(-x) tommy1729 2 6,769 12/11/2014, 11:59 PM Last Post: tommy1729 [number theory] sieving with a_i mod p_i tommy1729 7 17,375 09/12/2014, 07:28 AM Last Post: tommy1729 fake id(x) for better 2sinh method. tommy1729 5 11,714 06/05/2014, 08:21 AM Last Post: tommy1729

Users browsing this thread: 1 Guest(s)