# Rieman Zeta

1. Dec 11, 2008

### Sam1234

1. The problem statement, all variables and given/known data
Evaluate $P\int_{-\infty}^{\infty}\exp(imx^2}dx$, $m>0$.

2. Relevant equations
None

3. The attempt at a solution
Consider the following contour $C$ consisting of
$C_1:=\{z=x+iy:y=0, x:-s \to s\}$
$C_2:=\{z=x+iy:x=0, y:0 \to is\}$
$C_3:=\{z=x+iy:x: s \to -s, y: is \to -is \}$
$C_4:=\{z=x+iy:x=0: y:-is \to 0\}$

This is where i am stuck
1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

2. Dec 11, 2008

### Sam1234

Sorry, i gave the wrong title

3. Dec 11, 2008

### mutton

Well, why was that contour chosen? Does the integral go to 0 on some segments?

4. Dec 11, 2008

### Sam1234

actually in C_2, x=s and in C_4, x=-s

5. Dec 11, 2008

### Sam1234

Ok, I worked so far as that it only remains to show that the integrals on C_2 and C_4 are zero. I suspect having to use an ML-bound but don't really know how to do this.