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Subdisciplines

Algebraic number field
A finite degree (and hence algebraic) field extension of the field of rational numbers
Algebraic number theory
Branch of number theory
Analytic number theory
Exploring properties of the integers with complex analysis
Class field theory
Branch of algebraic number theory concerned with abelian extensions
Dirichlet character
Certain arithmetic functions
Möbius inversion formula
Relation between pairs of arithmetic functions
Riemann hypothesis
Conjecture in mathematics linked to the distribution of prime numbers