# Lucile Devin: Chebyshev’s bias and sums of two squares

**Time: **
Fri 2021-06-11 13.30 - 14.30

**Location: **
Zoom, meeting ID: 696 8725 5050

**Lecturer: **
Lucile Devin (Chalmers)

### Abstract

Studying the secondary terms of the Prime Number Theorem in Arithmetic Progressions, Chebyshev claimed that there are more prime numbers congruent to 3 modulo 4 than to 1 modulo 4. We will explain and qualify this claim following the framework of Rubinstein and Sarnak. Then we will see how this framework can be adapted to other questions on the distribution of prime numbers. This will be illustrated by a new Chebyshev-like claim : "for more than half of the prime numbers that can be written as a sum of two square, the odd square is the square of a positive integer congruent to 1 mod 4".