# The Riemann Hypothesis

Ameya Pitale

Our own Dr. Ameya Pitale will be speaking on

Wednesday, March 2nd at 5pm in PHSC 1105

on the famous Riemann Hypothesis.

The Riemann zeta function is defined for any complex number, s, using an infinite series as:

Well, technically, this is not right since even your friend in Calc III knows (or at least should know!) that this series doesn’t converge if s is less than 1.  The above function is the Riemann Zeta function for s greater than 1, and then you have to use some complex analysis to define it for all other s values.

The Riemann hypothesis is then the conjecture that the only non-stupid zeros of the the function are when the real part of s is 1/2.  According to Wikipedia, 10,000,000,000,000 zeros have so far been found and all of them are where they should be.  If you prove or disprove the Riemann hypothesis, then besides being as famous as Bat Boy (see below), you’ll earn yourself a million bucks.

Here’s a cool video which shows you what we mean:

Dr. Pitale will tell us all about the math involved and why the Riemann Zeta function is so darned important:

I am sure that students have often wondered while studying sequence and series in a Calculus 3 class as to the need and usefulness of the material.  I would like to start with some very simple questions whose answers lead naturally to understanding certain series. These series are special cases of a very famous function in number theory and all of math – the Riemann Zeta function. This function is full of rich information about prime numbers and studying it gives us deep insights into some very difficult questions in number theory. And if you are really smart and very very hard working, then it can also lead you to a million dollars.

– Dr. Pitale’s abstract

Or, xkcd’s take on it: