Tag Archives: zeta

The Riemann zeta function and prime numbers

Posted on March 6, 2017 by Brent

In a previous post I defined the famous Riemann zeta function, Today I want to give you a glimpse of what it has to do with prime numbers—which is a big part of why it is so famous. Consider the … Continue reading →

Posted in number theory | Tagged , , , , | 15 Comments

The Basel problem

Posted on February 6, 2017 by Brent

I wanted to follow up on something I mentioned in my previous post: I claimed that At the time I didn’t know how to prove this, but I did some quick research and today I’m going to explain it! It … Continue reading →

Posted in infinity, number theory | Tagged , , , , , | 9 Comments

The Riemann zeta function

Posted on February 2, 2017 by Brent

Recall from my previous post that given a function , we define , the Dirichlet generating function of , by We also proved that : the product of Dirichlet generating functions is the Dirichlet generating function of the Dirichlet convolution. … Continue reading →

Posted in number theory | Tagged , , , , , , , | 2 Comments

Dirichlet generating functions

Posted on January 30, 2017 by Brent

Suppose is a function defined for positive integers . Then we can define an infinite series as follows: (This might look a bit strange, but bear with me!) For example, suppose for all . Then (Note that in this case, … Continue reading →

Posted in number theory | Tagged , , , , , , , | 5 Comments