Joni's Math Notes

In this post, we discuss divergence results of Fourier series; this previous post was about convergence results. We showed earlier that qui...

In this post, we consider cyclotomic polynomials, which are a special class of polynomials with various connections to number theory, algebr...

In this post, we discuss some non-trivial convergence results for Fourier series. Convergence questions for Fourier series have been histo...

We derive the basic properties of Fourier series in this post and apply them to prove some elegant sum and product identities, namely a  for...

In later posts, we consider properties of Fourier series (for instance, convergence and divergence results), as well as lacunary trigonomet...

In this post we prove the existence of primitive roots modulo prime powers, using elementary number theory and presenting numerous problems ...