New Perspective On The Riemann Hypothesis Vincent Granville by Vincent Granville instant download after payment.

This tutorial provides a solid introduction to the Generalized Riemann Hypothesis and related functions, including Dirichlet series, Euler products, non-integer primes (Beurling primes), Dirichlet characters and Rademacher random multiplicative functions. The topic is usually explained in obscure jargon or inane generalities. To the contrary, this article will intrigue you with the beauty and power of this theory. The summary style is very compact, covering much more than traditionally taught in a first graduate course in analytic number theory. The choice of the topics is a little biased, with an emphasis on probabilistic models. My approach, discussing the “hole of the orbit” – called the eye of the Riemann zeta function in a previous article – is particularly intuitive.

The accompanying Python code covers a large class of interesting functions to allow you to perform as many different experiments as possible. If you are interested to know a lot more than the basics and possibly investigate this conjecture using machine learning techniques, this article is for you. The Python code also shows you how to produce beautiful videos of the various functions involved, in particular their orbits. This visual exploration shows that the Riemann zeta function (based on the trivial character χ), and a specific Dirichlet-L function (based on the non-trivial character χ4), behave very uniquely and similarly, explaining the connection between the Riemann and the Generalized Riemann Hypothesis, in pictures and videos rather than words.