# An introductory course on RH.

1. May 19, 2010

### 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.

2. Jul 7, 2010

### Eynstone

If you mean to say Riemann Hypothesis by 'RH' ,here's a good book:
Prime Obsession (by J. Derbyshire).

3. Jul 9, 2010

### zetafunction

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 $$N(E)= \frac{1}{\pi}Arg \xi(1/2+iE)$$

4. Jul 9, 2010

### jackmell

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.

5. Jul 9, 2010

6. Aug 9, 2010

### Major_Energy

I'll second this, just finishing it up actually.