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

Emil Artin (18981962) was a very influential mathematician
who made major contributions to mathematics and
in particular to number theory. His ancestors came
from Armenia. This school is held on the occasion of
his 120th birthday and will be followed by the
Emil Artin International Conference (this is a research
conference). The school focuses on some of Artin's contributions to number theory and representation theory and in particular on two famous conjectures he made: the Artin primitive root conjecture and the Artin holomorphy conjecture. Despite Artin's efforts (and those of many other number theorists!) his conjectures remain unsolved in their full generality. The school does not aim to present the state of the art of work on these conjectures, but focuses on basic ideas and methods that are also very important in number theory beyond these two conjectures. Topics that will be covered include: Groups and algebraic methods in number theory, in particular the splitting of primes in number fields, the Frobenius symbol, the Chebotarev density theorem and complex representations of finite groups. The Riemann zeta function and its generalizations (in particular, Dirichlet Lfunctions, Dedekind zetafunctions and Artin Lfunctions) Applications of zeta functions in analytic number theory (such as counting primes in arithmetic progression). Artin's primitive root conjecture and Hooley's conditional proof assuming the Generalized Riemann Hypothesis. Artin's and Brauer's theorems on induced characters and their application to the Artin holomorphy conjecture. 