Search results

#REDIRECT[[Algebraic number field]] [[Category:Theorems in number theory]] ...

[[:Category:Category theory|Category theory]] | [[:Category:Chaos theory|Chaos theory]] | ...

{{short description|Result that expresses a function f(x + y) in terms of f(x) and f(y)}} {{About|addition theorems in general|specific addition theorems for trigonometric functions|angle addition formulas}} ...

* [[Riemann–Hurwitz formula]] in algebraic geometry * [[Hurwitz's theorem (number theory)]] ...

...m of curves]] describes classification of [[Regular curve|regular curves]] in space up to [[Translation (geometry)|translation]] and [[rotation]]. ...as a stepping stone to a larger result, rather than as a useful statement in-and-of itself. ...

...)|signature]] of the [[intersection theory|intersection pairing]] on the [[algebraic curve]]s ''C'' on ''V''. It says, roughly speaking, that the space spanned ...H'' be the [[divisor class]] on ''V'' of a [[hyperplane section]] of ''V'' in a given [[projective embedding]]. Then the intersection ...

{{short description|One of several theorems linking the sizes of different ideal class groups}} {{For|reflection principles in set theory|Reflection principle}} ...

...are the curves.<ref>James S. Milne, ''Jacobian Varieties'', Corollary 12.2 in {{Harvtxt|Cornell|Silverman|1986}}</ref> ...rieties]], is [[injective]] (on [[geometric point]]s). Generalizations are in two directions. Firstly, to geometric questions about that morphism, for ex ...

...rovides an asymptotic formula for counting the number of prime ideals of a number field}} ...des an asymptotic formula for counting the number of [[prime ideal]]s of a number field ''K'', with [[field norm|norm]] at most ''X''. ...

...alysis''' is the practice of looking at a problem relative to each [[prime number]] ''p'' first, and then later trying to integrate the information gained at ==Group theory== ...

{{short description|Theorem in class field theory on mappings induced by extending ideals}} {{about|the Hauptidealsatz of class field theory|the theorem about Noetherian rings| Krull's principal ideal theorem}} ...

{{short description|In cyclic extension of number fields, if k is a local norm everywhere, it is a global norm}} ...'''Hasse norm theorem''' states that if L/K is a [[cyclic extension]] of [[number field]]s, then if a nonzero element of K is a local norm everywhere, then i ...

{{short description|Concerns the class number of a real quadratic field of discriminant > 0}} ...of [[discriminant]] ''d''&nbsp;>&nbsp;0. If the [[Fundamental unit (number theory)|fundamental unit]] of the field is ...

{{short description|On power series with rational coefficients that are algebraic functions}} ...of any [[power series]] which is an [[algebraic function]] with [[rational number]] coefficients. Through the theorem, it is readily demonstrable, for exampl ...

{{Short description|Theorems generalizing the Brouwer fixed-point theorem}} ...atics]], a number of '''[[fixed point (mathematics)|fixed-point]] theorems in infinite-dimensional spaces''' generalise the [[Brouwer fixed-point theorem ...

...n]] of the field <math>K=k(x_1,\dots,x_n)</math> of [[rational functions]] in <math>n</math> variables over <math>k</math>. ...math> (with degree 3 over <math>k(y)</math>). We see that the degree of an algebraic function field is not a well-defined notion. ...

...2. Its [[Graph automorphism|automorphism group]] has 120 elements, and is in fact the [[symmetric group]] <math>S_5</math>.]] ...graph theory, involving the use of [[linear algebra]], the use of [[group theory]], and the study of [[graph property|graph invariants]]. ...

{{short description|Theorem in the representation theory of linear algebraic groups}} ...lchin theorem''' is a theorem in the [[representation theory]] of [[linear algebraic group]]s; '''[[Lie's theorem]]''' is the analog for [[linear Lie algebra]]s ...

{{short description|Number of connected components an algebraic curve can have}} ...algebraic curve of degree {{mvar|m}} in the real [[projective plane]], the number of components {{mvar|c}} is bounded by ...

...ion|Finitely many for a smooth algebraic curve of genus > 0 defined over a number field}} ...greater than zero has only finitely many integral points over any given [[number field]]. ...