Linnik's theorem : a comparison of the classical and the pretentious approach
The goal of this master's thesis is to understand Linnik's theorem, which gives us an upper bound for the first prime number in an arithmetic progression. We will analyze and compare two distinct methods: the classical approach and the pretentious approach. The first one relies on zeros of Dirichlet L-functions. The second one is based on Halász's theorem and distance functions. It was developped by Granville annd Soundarajan.
Linnik Zeros of Dirichlet L-functions Pretentiousness Halasz's theorem