In mathematics, an L-function is a meromorphic function on the complex plane, associated to one out of several categories of mathematical objects. An L-series is a Dirichlet series, usually convergent on a half-plane, that may give rise to an L-function via analytic continuation. The Riemann zeta function is an example of an L-function, and one important conjecture involving L-functions is the Riemann hypothesis and its generalization. The theory of L-functions has become a very substantial, and still largely conjectural, part of contemporary analytic number theory. In it, broad generalisations of the Riemann zeta function and the L-series for a Dirichlet character are constructed, and their general properties, in most cases still out of reach of proof, are set out in a systematic way. Because of the Euler product formula there is a deep connection between L-functions and the theory of prime numbers. The mathematical field that studies L-functions is sometimes called analytic theory of L-functions. (Wikipedia).
Introduction to Linear Functions and Slope (L10.1)
This lesson introduces linear functions, describes the behavior of linear function, and explains how to determine the slope of a line given two points. Video content created by Jenifer Bohart, William Meacham, Judy Sutor, and Donna Guhse from SCC (CC-BY 4.0)
From playlist Introduction to Functions: Function Basics
Definition of a Surjective Function and a Function that is NOT Surjective
We define what it means for a function to be surjective and explain the intuition behind the definition. We then do an example where we show a function is not surjective. Surjective functions are also called onto functions. Useful Math Supplies https://amzn.to/3Y5TGcv My Recording Gear ht
From playlist Injective, Surjective, and Bijective Functions
From playlist Abstract Algebra 1
What is an Injective Function? Definition and Explanation
An explanation to help understand what it means for a function to be injective, also known as one-to-one. The definition of an injection leads us to some important properties of injective functions! Subscribe to see more new math videos! Music: OcularNebula - The Lopez
From playlist Functions
Andrew Sutherland, Arithmetic L-functions and their Sato-Tate distributions
VaNTAGe seminar on April 28, 2020. License: CC-BY-NC-SA Closed captions provided by Jun Bo Lau.
From playlist The Sato-Tate conjecture for abelian varieties
Sample exam problems on the heat equation and the Laplace equation.
From playlist MATH2018 Engineering Mathematics 2D
Oxford Calculus: Fourier Series Derivation
University of Oxford Mathematician Dr Tom Crawford explains how to derive the Fourier Series coefficients for any periodic function. Accompanying FREE worksheet courtesy of Maple Learn here: https://learn.maplesoft.com/d/DLEJJJNPPUILFLPNCTLRGSJHCTMHCRDJCTAUIRKKGSGPBSFHJNIFNRPODNPFBLJROIHMN
From playlist Oxford Calculus
Neural Networks – back propagation (training) Full project: https://github.com/Atcold/torch-Video-Tutorials Notes: 09:08 – 𝓛(ϴ) can be written as J(ϴ) or J(θ) 37:55 – in equation v), a⁽ˡ⁾ should be â⁽ˡ⁾ 40:54 – some transpositions are missing: ϴ → ϴ + ηδâᵀ (check next video for an in-dept
From playlist Deep-Learning-Course
V8-7: Half Range Extensions, Fourier sin/cosine series, Elementary Differential equations
V8-7: Half Range Extensions, Fourier sin/cosine series, Example of sawtooth waves and triangle waves. Elementary Differential equations Course playlist: https://www.youtube.com/playlist?list=PLbxFfU5GKZz0GbSSFMjZQyZtCq-0ol_jD
From playlist Elementary Differential Equations
Connecting Function Limits and Sequence Limits | Real Analysis
We prove the limit of a function f as x approaches c is L if and only if the sequence of images of a_n converges to L for all sequences a_n in the domain of f where each a_n is not equal to c. Our bidirectional proof will begin with a direct proof, using the epsilon delta definition of the
From playlist Real Analysis
This talk is about the Riemann Roch theorem for genus 1 curves. We check the Riemann Roch theorem explicitly by using elliptic functions to find periodic functions with given divisors. We use this to show that the ring of functions on an affine elliptic curve is not a unique factorizati
From playlist Algebraic geometry: extra topics
021 Even further Orbital Angular Momentum - Eigenfunctions, Parity and Kinetic Energy
In this series of physics lectures, Professor J.J. Binney explains how probabilities are obtained from quantum amplitudes, why they give rise to quantum interference, the concept of a complete set of amplitudes and how this defines a "quantum state". Notes and problem sets here http://www
From playlist James Binney - 2nd Year Quantum Mechanics
Let's Learn Physics: Good Vibrations from Wave Equations
The wave equation is not only important due to the fact that it describes many different physical phenomena, but also because it naturally leads us to some very interesting mathematical results and techniques. In this stream, we will talk about methods we can use to solve the wave equation
From playlist Let's Learn (Classical) Physics: ZAP Physics Livestreams
Define linear functions. Use function notation to evaluate linear functions. Learn to identify linear function from data, graphs, and equations.
From playlist Algebra 1