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# Tag Archives: Riemann

## The Basel problem

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

## The Riemann zeta function

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 convolution, Dirichlet, inversion, moebius, mu, primes, Riemann, zeta
1 Comment

## Dirichlet generating functions

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 convolution, Dirichlet, inversion, moebius, mu, primes, Riemann, zeta
3 Comments