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ramification function

См. также в других словарях:

  • Ramification — In mathematics, ramification is a geometric term used for branching out , in the way that the square root function, for complex numbers, can be seen to have two branches differing in sign. It is also used from the opposite perspective (branches… …   Wikipedia

  • Hasse-Weil zeta function — In mathematics, the Hasse Weil zeta function attached to an algebraic variety V defined over a number field K is one of the two most important types of L function. Such L functions are called global , in that they are defined as Euler products in …   Wikipedia

  • Algebraic number field — In mathematics, an algebraic number field (or simply number field) F is a finite (and hence algebraic) field extension of the field of rational numbers Q. Thus F is a field that contains Q and has finite dimension when considered as a vector… …   Wikipedia

  • Riemann-Hurwitz formula — In mathematics, the Riemann Hurwitz formula, named after Bernhard Riemann and Adolf Hurwitz, describes the relationship of the Euler characteristics of two surfaces when one is a ramified covering of the other. It therefore connects ramification… …   Wikipedia

  • Prime number — Prime redirects here. For other uses, see Prime (disambiguation). A prime number (or a prime) is a natural number greater than 1 that has no positive divisors other than 1 and itself. A natural number greater than 1 that is not a prime number is… …   Wikipedia

  • Discriminant of an algebraic number field — A fundamental domain of the ring of integers of the field K obtained from Q by adjoining a root of x3 − x2 − 2x + 1. This fundamental domain sits inside K ⊗QR. The discriminant of K is 49 = 72.… …   Wikipedia

  • Conductor (class field theory) — In algebraic number theory, the conductor of a finite abelian extension of local or global fields provides a quantitative measure of the ramification in the extension. The definition of the conductor is related to the Artin map. Contents 1 Local… …   Wikipedia

  • Discriminant — In algebra, the discriminant of a polynomial is an expression which gives information about the nature of the polynomial s roots. For example, the discriminant of the quadratic polynomial is Here, if Δ > 0, the polynomial has two real roots,… …   Wikipedia

  • Hyperelliptic curve — In algebraic geometry, a hyperelliptic curve (over the complex numbers) is an algebraic curve given by an equation of the form:y^2 = f(x)where f(x) is a polynomial of degree n > 4 with n distinct roots. A hyperelliptic function is a function from …   Wikipedia

  • Hurwitz's theorem — In mathematics, Hurwitz s theorem is any of at least five different results named after Adolf Hurwitz. Hurwitz s theorem in complex analysis In complex analysis, Hurwitz s theorem roughly states that, under certain conditions, if a sequence of… …   Wikipedia

  • Projective line — In mathematics, a projective line is a one dimensional projective space. The projective line over a field K , denoted P1( K ), may be defined as the set of one dimensional subspaces of the two dimensional vector space K 2 (it does carry other… …   Wikipedia

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