RH Saga I

This is the main page for the PeakMath course RH Saga I (Cosmology of L-functions), which will follow Season 1 on YouTube quite closely, but going into much more detail. The aim is to give an overview of the world of L-functions, an introduction to the Riemann Hypothesis and other immortal problems, and some first steps in the story about the field with one element, the mythical and conjectural theory that might lead to solutions of some of these immortal problems.

The course will run from May to late August or so (in 2026), during which time I will publish the main storyline as individual Chapters, and a number of smaller posts on various side topics connected to the main story.

One of the main things I want to give you in this course is the experience of exploring open problems on your own. As I'm envisioning these problems now, I will group them into Exploring primes, Exploring degree 1 L-functions (mostly quadratic Dirichlet L-functions), and Exploring degree 2 L-functions (primarily those coming from elliptic curves). I will also share a carefully selected research talk each weekend, to give you a sense of the research frontier.

Chapters published so far

Chapter 1: The Dream of a Field with One Element

Chapter 2: Langlands and the Landscape of L-functions

Chapter 3: What does the Generalized Riemann Hypothesis really mean?