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# Monthly Archives: January 2017

## 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
5 Comments

## More fun with Dirichlet convolution

I’m back after a bit of a hiatus for the holidays! Last time we saw how the principle of Möbius inversion arises from considering the function from the point of view of Dirichlet convolution. Put simply, the Möbius function is … Continue reading

Posted in number theory
Tagged arithmetic, convolution, Dirichlet, divisors, inversion, moebius, mu
1 Comment

## Paper torus with Villarceau circles

I made another thing! This is a torus, made from 24 crescent-shaped pieces of paper with slots cut into them so they interlock with each other. I followed these instructions on cutoutfoldup.com. There is also a template with some ideas … Continue reading