Arithmetic equivalence through Galois representations

Abstract

"An important objective in Algebraic number theory is the study of number fields and their ring Of algebraic integers. One of the crucial arithmetic invariants associated with a number field K is its Dedekind zeta function? This function is the natural generalization of the Riemann zeta function and gives us arithmetic information about the number field. For example, if we compute its residue at the isolated singularity l, we get a formula for the order of the class group, in the case of non real quadratic fields". -- Tomado del abstract