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An introductory course on RH.

  1. May 19, 2010 #1
    Does someone know if there's a course offered on RH?

    I mean reading the literature can be quite intimidating without some beckground before, I read somewhere that the prof from purdue (who allegedlly proved RH) was contemplating offering such a course, but didn't offer such a course.
  2. jcsd
  3. Jul 7, 2010 #2
    If you mean to say Riemann Hypothesis by 'RH' ,here's a good book:
    Prime Obsession (by J. Derbyshire).
  4. Jul 9, 2010 #3
    a phycisist approach to RH , is a bit simpler it use the approximate asymptotic formula

    [tex] f^{-1} (x) = \sqrt (4\pi ) \frac{d^{-1/2}g(x)}{dx^{-1/2}} [/tex]

    this formula is valid only for one spatial dimension (x,t) , so the conjectured WKB approximation for the inverse of the potential inside the Hamiltonian

    [tex] -D^{2}+f(x) [/tex] with D meaning derivative respect to 'x' is

    [tex] \pi f^{-1}(x) = \int_{0}^{x} \frac{g(t)dt}{(x-t)^{1/2}} [/tex]

    with [tex] g(s)= (-i)^{1/2}\frac{ \xi ' (1/2+is)}{\xi(1/2+is)}+(i)^{1/2}\frac{ \xi ' (1/2-is)}{\xi(1/2-is)} [/tex]

    since for RH [tex] g(s)= dN(s) [/tex] and [tex] N(E)= \frac{1}{\pi}Arg \xi(1/2+iE) [/tex]
  5. Jul 9, 2010 #4
    I think I would be interested in working on such a project although I think it would be better titled as the zeta function and approached through a strong foundation in Complex Analysis. I'm not an expert though.
  6. Jul 9, 2010 #5

    One of my favorite papers on it, not sure if it's your level, but it's a fascinating look at the structure of zeta(s).
  7. Aug 9, 2010 #6
    I'll second this, just finishing it up actually.
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