Emil Artin International School in Mathematics for Students
A proposal for a Wams school on
The mathematics of Artin's conjectures
Yerevan State University, Yerevan, Armenia
May 21 th- 25th, 2018



Groups and algebraic methods in number theory
Valerio Talamanca
  • (Z/pZ)* is a cyclic group, its occurrence as cyclotomic Galois group.
  • Explicit Galois theory: quadratic fields are cyclotomic (Gauss sums), Kronecker-Weber Theorem
Zeta functions and L-functions
Francesco Pappalardi
  • Riemann zeta-function, prime number theorem.
  • Dirichlet- L-functions, primes in arithmetic progressions.
  • Dedekind-zeta-function, prime number theorem for number fields.
  • Artin-L-functions: meromorphy (by Artin- Brauer) and conjectured holomorphy
Complex representations of finite groups
Lilit Martirosyan
  • Linear representation and characters
  • Induced characters
  • Artin's and Brauer's theorem on induced characters.
Algebraic Number Theory
Peter Stevenhagen
  • Splitting of primes in number fields, densities.
  • Frobenius symbol, Chebotarev density theorem.
  • Character sum method for Artin type densities.
Hooley's proof of the Artin primitive root conjecture
Pieter Moree
  • Artin's primitive root conjecture. Approach by heuristics, quadratic correction.
  • Hooley's 1967 proof under GRH.
  • Applications.
Exercise Session

Every afternoon from 5pm to 6pm (except Wednesday) there will be an exercise session where the participants will solve problems assigned by the lecturers.