Zeros and Primes

Prerequisites for this post: previous post, and complex analysis. For this entire post, $latex {s}&fg=000000$ is a complex variable with $latex {s = \sigma + it}&fg=000000$. 1. The $latex {\Gamma}&fg=000000$ function So there's this thing called the Gamma function. Denoted $latex {\Gamma(s)}&fg=000000$, it is defined by $latex \displaystyle \Gamma(s) = \int_0^{\infty} x^{s-1} e^{-x} \; dx… Continue reading Zeros and Primes

von Mangoldt and Zeta

Prerequisites for this post: definition of Dirichlet convolution, and big $latex {O}&fg=000000$-notation. Normally I don't like to blog about something until I'm pretty confident that I have a reasonably good understanding of what's happening, but I desperately need to sort out my thoughts, so here I go\dots 1. Primes One day, an alien explorer lands… Continue reading von Mangoldt and Zeta