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An example of an active area of research in algebraic number theory is Iwasawa theory. The Langlands program , one of the main current large-scale research plans in mathematics, is sometimes described as an attempt to generalise class field theory to non-abelian extensions of number fields.
Composite number. Highly composite number; Even and odd numbers. Parity; Divisor, aliquot part. Greatest common divisor; Least common multiple; Euclidean algorithm; Coprime; Euclid's lemma; Bézout's identity, Bézout's lemma; Extended Euclidean algorithm; Table of divisors; Prime number, prime power. Bonse's inequality; Prime factor. Table of ...
number theory: Dorin Andrica: 45 Artin conjecture (L-functions) number theory: Emil Artin: 650 Artin's conjecture on primitive roots: number theory: ⇐generalized Riemann hypothesis [2] ⇐Selberg conjecture B [3] Emil Artin: 325 Bateman–Horn conjecture: number theory: Paul T. Bateman and Roger Horn: 245 Baum–Connes conjecture: operator K ...
Traditionally, number theory is the branch of mathematics concerned with the properties of integers and many of its open problems are easily understood even by non-mathematicians. More generally, the field has come to be concerned with a wider class of problems that arise naturally from the study of integers.
1. The class number of a number field is the cardinality of the ideal class group of the field. 2. In group theory, the class number is the number of conjugacy classes of a group. 3. Class number is the number of equivalence classes of binary quadratic forms of a given discriminant. 4. The class number problem. conductor
Brun–Titchmarsh theorem (number theory) Carmichael's theorem (Fibonacci numbers) Chebotarev's density theorem (number theory) Chen's theorem (number theory) Chowla–Mordell theorem (number theory) Cohn's irreducibility criterion (polynomials) Critical line theorem (number theory) Davenport–Schmidt theorem (number theory, Diophantine ...
In number theory, Euler's theorem (also known as the Fermat–Euler theorem or Euler's totient theorem) states that, if n and a are coprime positive integers, then () is congruent to modulo n, where denotes Euler's totient function; that is
Almgren–Pitts min-max theory; Approximation theory; Arakelov theory; Asymptotic theory; Automata theory; Bass–Serre theory; Bifurcation theory; Braid theory