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v t e Number theory
Fields	Algebraic number theory ( class field theory, non-abelian class field theory, Iwasawa theory, Iwasawa–Tate theory, Kummer theory) Analytic number theory ( analytic theory of L-functions, probabilistic number theory, sieve theory) Geometric number theory Computational number theory Transcendental number theory Diophantine geometry ( Arakelov theory, Hodge–Arakelov theory) Arithmetic combinatorics ( additive number theory) Arithmetic geometry ( anabelian geometry, P-adic Hodge theory) Arithmetic topology Arithmetic dynamics
Key concepts	Numbers 0 Natural numbers Unity Prime numbers Composite numbers Rational numbers Irrational numbers Algebraic numbers Transcendental numbers P-adic numbers ( P-adic analysis) Arithmetic Modular arithmetic Chinese remainder theorem Arithmetic functions
Advanced concepts	Quadratic forms Modular forms L-functions Diophantine equations Diophantine approximation Continued fractions
Category List of topics List of recreational topics Wikibook Wikiversity

v t e Number theory
Fields	Algebraic number theory ( class field theory, non-abelian class field theory, Iwasawa theory, Iwasawa–Tate theory, Kummer theory) Analytic number theory ( analytic theory of L-functions, probabilistic number theory, sieve theory) Geometric number theory Computational number theory Transcendental number theory Diophantine geometry ( Arakelov theory, Hodge–Arakelov theory) Arithmetic combinatorics ( additive number theory) Arithmetic geometry ( anabelian geometry, P-adic Hodge theory) Arithmetic topology Arithmetic dynamics
Key concepts	Numbers 0 Natural numbers Unity Prime numbers Composite numbers Rational numbers Irrational numbers Algebraic numbers Transcendental numbers P-adic numbers ( P-adic analysis) Arithmetic Modular arithmetic Chinese remainder theorem Arithmetic functions
Advanced concepts	Quadratic forms Modular forms L-functions Diophantine equations Diophantine approximation Continued fractions
Category List of topics List of recreational topics Wikibook Wikiversity