 Hilbert's twelfth problem

Hilbert's twelfth problem, proposed by the mathematician David Hilbert in 1900, is concerned with the theory of functions with respect to algebraic number fields and involves the study of the so-called "absolutely abelian extensions" of these fields. More specifically, the problem asks for a systematic method to construct all the abelian extensions of a given number field using explicit functions, particularly through the use of modular forms.