Mediaspace scheduled maintenance: Aug 25, 2026 07:00 - 12:00 AM. During this time, videos will be temporarily unavailable. Check status updates.

Lecture

Analytic Continuation of Zeta Function

In course

MATH-201: Analysis III

Calcul différentiel et intégral. Eléments d'analyse complexe. ...

Description

This lecture covers the analytic continuation of the zeta function, regularization of the sum of natural numbers, and the relationship between the zeta function and holomorphic functions. The instructor discusses the concept of holomorphy, the properties of the zeta function, and the relation between the zeta function and natural numbers.

This video is available exclusively on Mediaspace for a restricted audience. Please log in to MediaSpace to access it if you have the necessary permissions.

Watch on Mediaspace

Instructors (2)

Marco Picasso

Joachim Stubbe

Official source

Ontological neighbourhood

Mathematics

Analysis: Complex analysis

Related concepts (32)

Bamboo

Bamboos are a diverse group of mostly evergreen perennial flowering plants making up the subfamily Bambusoideae of the grass family Poaceae. Giant bamboos are the largest members of the grass family, in the case of Dendrocalamus sinicus individual culms reaching a length of 46 meters, up to 36 centimeters in thickness and a weight of up to 450 kilograms. The internodes of bamboos can also be of great length. Kinabaluchloa wrayi has internodes up to 2.5 meters in length.

Toilet paper

Toilet paper (sometimes called toilet tissue or bathroom tissue) is a tissue paper product primarily used to clean the anus and surrounding region of feces (after defecation), and to clean the external genitalia and perineal area of urine (after urination). It is usually supplied as a long strip of perforated paper wrapped around a paperboard core for storage in a dispenser near a toilet. The bundle, or roll of toilet paper, is known as a toilet roll, or loo roll or bog roll in Britain.

Binary relation

In mathematics, a binary relation associates elements of one set, called the domain, with elements of another set, called the codomain. A binary relation over sets X and Y is a new set of ordered pairs (x, y) consisting of elements x in X and y in Y. It is a generalization of the more widely understood idea of a unary function. It encodes the common concept of relation: an element x is related to an element y, if and only if the pair (x, y) belongs to the set of ordered pairs that defines the binary relation.

Function of several complex variables

The theory of functions of several complex variables is the branch of mathematics dealing with functions defined on the complex coordinate space , that is, n-tuples of complex numbers. The name of the field dealing with the properties of these functions is called several complex variables (and analytic space), which the Mathematics Subject Classification has as a top-level heading. As in complex analysis of functions of one variable, which is the case n = 1, the functions studied are holomorphic or complex analytic so that, locally, they are power series in the variables zi.

Converse relation

In mathematics, the converse relation, or transpose, of a binary relation is the relation that occurs when the order of the elements is switched in the relation. For example, the converse of the relation 'child of' is the relation 'parent of'. In formal terms, if and are sets and is a relation from to then is the relation defined so that if and only if In set-builder notation, The notation is analogous with that for an inverse function. Although many functions do not have an inverse, every relation does have a unique converse.

Related lectures (33)

Optimization Problems: Algebra and Trinomial Equations

Explores optimization problems in algebra and trinomial equations, focusing on maximizing area with fixed perimeters.

Topology of Riemann Surfaces

Covers the topology of Riemann surfaces, focusing on orientation and orientability.

Graph and Diagonal

Discusses the graph of a relation and the concept of separation.

Surfaces: The Torus

Explores the definition of surfaces, focusing on the torus and its construction through various examples and morphic images.

Linear Approximation and Derivative Parametric