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A local zeta-function is a generating function for the number of points on an algebraic variety V over a finite field F, over the finite field extensions of F. According to the Weil conjectures (q.v.) these functions, for non-singular varieties, exhibit properties closely analogous to the Riemann zeta-function , including the Riemann hypothesis .
Analytic continuation of natural logarithm (imaginary part) Analytic continuation is a technique to extend the domain of a given analytic function.Analytic continuation often succeeds in defining further values of a function, for example in a new region where an infinite series representation in terms of which it is initially defined becomes divergent.
Recursion is the definition of a function invoking itself. A definition containing itself inside itself, by value, leads to the whole value being of infinite size. Other notations which support recursion natively overcome this by referring to the function definition by name. Lambda calculus cannot express this: all functions are anonymous in ...
Algebraic geometry is a branch of mathematics which uses abstract algebraic techniques, mainly from commutative algebra, to solve geometrical problems. Classically, it studies zeros of multivariate polynomials ; the modern approach generalizes this in a few different aspects.
Modern foundations of algebraic geometry were developed based on contemporary commutative algebra, including valuation theory and the theory of ideals by Oscar Zariski and others in the 1930s and 1940s. [11] In 1949, André Weil posed the landmark Weil conjectures about the local zeta-functions of algebraic varieties over finite fields. [12]
In mathematics, algebraic geometry and analytic geometry are two closely related subjects. While algebraic geometry studies algebraic varieties, analytic geometry deals with complex manifolds and the more general analytic spaces defined locally by the vanishing of analytic functions of several complex variables. The deep relation between these ...
In mathematics, in particular algebraic geometry, a moduli space is a geometric space (usually a scheme or an algebraic stack) whose points represent algebro-geometric objects of some fixed kind, or isomorphism classes of such objects.
In mathematics, an algebraic function is a function that can be defined as the root of an irreducible polynomial equation. Algebraic functions are often algebraic expressions using a finite number of terms, involving only the algebraic operations addition, subtraction, multiplication, division, and raising to a fractional power. Examples of ...
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