# an introductory course on RH.

by MathematicalPhysicist
Tags: introductory
 P: 3,128 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.
 P: 336 If you mean to say Riemann Hypothesis by 'RH' ,here's a good book: Prime Obsession (by J. Derbyshire).
 P: 399 a phycisist approach to RH , is a bit simpler it use the approximate asymptotic formula $$f^{-1} (x) = \sqrt (4\pi ) \frac{d^{-1/2}g(x)}{dx^{-1/2}}$$ 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 $$-D^{2}+f(x)$$ with D meaning derivative respect to 'x' is $$\pi f^{-1}(x) = \int_{0}^{x} \frac{g(t)dt}{(x-t)^{1/2}}$$ with $$g(s)= (-i)^{1/2}\frac{ \xi ' (1/2+is)}{\xi(1/2+is)}+(i)^{1/2}\frac{ \xi ' (1/2-is)}{\xi(1/2-is)}$$ since for RH $$g(s)= dN(s)$$ and $$N(E)= \frac{1}{\pi}Arg \xi(1/2+iE)$$
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## an introductory course on RH.

 Quote by MathematicalPhysicist 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.
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.
 P: 241 http://arxiv.org/PS_cache/math/pdf/0309/0309433v1.pdf 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).
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 Quote by Eynstone If you mean to say Riemann Hypothesis by 'RH' ,here's a good book: Prime Obsession (by J. Derbyshire).
I'll second this, just finishing it up actually.

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