The Distribution of Prime Numbers Spring 2025

Lecturer
Vivian Kuperberg
Coordinator
N/A

Lectures

Wednesdays, 8 to 10 in HG D 5.2
Fridays, 12 to 14 in HG D 1.1.
Exercise classes will be held on average once every two weeks, usually during the Wednesday lecture. They will be announced in class and below.

Lecture notes and recordings


Lectures notes are available here (Version of 21.2.2025). Lectures will be recorded and videos (internal to ETH) will be posted here.

Exercises

The lecture will be accompanied by roughly biweekly exercise classes, usually during the Wednesday class. I will announce the precise dates in the lecture as well as here.

Dates of exercise classes
February 26
Exercise sheet Solutions
Exercise sheet 1

Summary of the lectures

We indicate here the topics discussed in each lecture.
DayContent
19.2.2025 The Cram\'er model; example Cram\'er conjectures for prime numbers, specifically distribution of gaps, maximal gaps, Riemann Hypothesis.
21.2.2025 The Hardy--Littlewood k-tuple conjectures, consequences for distribution of primes in short intervals. Singular series constants are 1 on average.

Literature