an introductory course on RH.


by MathematicalPhysicist
Tags: introductory
MathematicalPhysicist
MathematicalPhysicist is offline
#1
May19-10, 05:53 AM
P: 3,170
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.
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Eynstone
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#2
Jul7-10, 12:15 AM
P: 336
If you mean to say Riemann Hypothesis by 'RH' ,here's a good book:
Prime Obsession (by J. Derbyshire).
zetafunction
zetafunction is offline
#3
Jul9-10, 05:24 AM
P: 399
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]

jackmell
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#4
Jul9-10, 07:20 AM
P: 1,666

an introductory course on RH.


Quote Quote by MathematicalPhysicist View Post
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.
Max™
Max™ is offline
#5
Jul9-10, 03:39 PM
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).
Major_Energy
Major_Energy is offline
#6
Aug9-10, 09:44 PM
P: 25
Quote Quote by Eynstone View Post
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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