Lectures notes are available here (Version of 16.4.2025). Lectures will be recorded and videos (internal to ETH) will be posted here.
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 |
| March 12 |
| March 26 |
| April 9 (note: I will be absent on April 9th; this will be a self-directed exercise session) |
| April 30 |
| Exercise sheet | Solutions |
|---|---|
| Exercise sheet 1 | |
| Exercise sheet 2 | |
| Exercise sheet 3 | |
| Exercise sheet 4 | |
| Exercise sheet 5 |
| Day | Content |
|---|---|
| 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. |
| 28.2.2025 | Sieve theory overview; the sieve of Eratosthenes; general sieve setup and examples. |
| 5.3.2025 | Brun's pure sieve |
| 7.3.2025 | Brun's sieve and the sum of the reciprocals of twin primes; Selberg's sieve introduction and Selberg's sieve for primes |
| 14.3.2025 | Selberg's sieve upper bound for primes; general statement of Selberg's sieve. |
| 19.3.2025 | Mean values of multiplicative functions; Rankin's trick. |
| 21.3.2025 | Brun--Titchmarsh; parity problem. Started on small gaps between primes. |
| 28.3.2025 | Small gaps between primes. GPY setup and definition of Maynard weights. |
| 2.4.2025 | Small gaps between primes, continued. Stated Bombieri--Vinogradov. |
| 4.4.2025 | Finished small gaps between primes; finding an optimal function. |
| 11.4.2025 | Circle method overview and intuition for Vinogradov's three primes; S(N,alpha) evaluated at various alpha. |