The Prime Numbers' Music, Staircase and Riemann Hypothesis¶

For DSP, mathematics is a fundamental tool to understand the different techniques. Hence, I'm also interested in different aspects of mathematics. And what aspect could be more "pure" mathematics than number theory and prime numbers? In this regard, to at least understand the still unsolved Riemann Hypothesis, where a price money of 1,000,000 will be given to the one who proves or disproves it, has been bothering me for quite some time. Despite a lot of material about the hypothesis being online, it was the book of Barry Mazur and William Stein entitled "Prime Numbers and the Riemann Hypothesis" which provided me at least a superficial understanding of it.

The nice thing about this book is its very simple approach, requiring not more than high school math. Each page contains graphs and illustrations of the analyzed functions and hence makes it quite easy to follow. Accordingly, it's a very nice book to get to know a bit about the Riemann Hypothesis (RH). However, admittedly, the mathematical treatment is intentionally quite superficial.

In this notebook, I do not want to directly talk about the RH. Instead, the notebook arose when I tried to replicate some calculations from the ...