Analytic number theory

Dirichlet density

In mathematics, the Dirichlet density (or analytic density) of a set of primes, named after Peter Gustav Lejeune Dirichlet, is a measure of the size of the set that is easier to use than the natural density. (Wikipedia).

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(ML 7.7.A1) Dirichlet distribution

Definition of the Dirichlet distribution, what it looks like, intuition for what the parameters control, and some statistics: mean, mode, and variance.

From playlist Machine Learning

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Theory of numbers: Dirichlet series

This lecture is part of an online undergraduate course on the theory of numbers. We describe the correspondence between Dirichlet series and arithmetic functions, and work out the Dirichlet series of the arithmetic functions in the previous lecture. Correction: Dave Neary pointed out t

From playlist Theory of numbers

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Astronomy - Ch. 9: Earth as a Planet (12 of 22) Earth's Density

Visit http://ilectureonline.com for more math and science lectures! In this video I will discuss the different density of the Earth: mantle, liquid core, and sold core. Next video in this series can be seen at: https://youtu.be/puI6el8sk14

From playlist ASTRONOMY 9 - EARTH AS A PLANET

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Physical Science 3.4b - Density

Density. The definition of density, the equation for density, and some numerical examples.

From playlist Physical Science Chapter 3 (Complete chapter)

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Physics - E&M: Ch 40.1 Current & Resistance Understood (16 of 17) What is Current Density?

Visit http://ilectureonline.com for more math and science lectures! In this video I will explain the current density, for example, of a conductor of a given current (I) and current density (J) is defined as the amount of current per unit area. Next video in this series can be seen at: ht

From playlist THE "WHAT IS" PLAYLIST

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Physics - E&M: Ch 40.1 Current & Resistance Understood (17 of 17) What is Current Density? Ex.

Visit http://ilectureonline.com for more math and science lectures! In this video I will find the current density, J=?, given current, I=4amps, and diameter, D=2mm. First video in this series can be seen at: https://youtu.be/bDe4lzgQY2E

From playlist THE "WHAT IS" PLAYLIST

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What is Density? | Gravitation | Physics | Don't Memorise

Understanding the concept of Density is very important in order to understand Physics. Watch this video to fully grasp the idea of density. To get access to the entire course based on Gravitation, enroll here: https://infinitylearn.com/microcourses?utm_source=youtube&utm_medium=Soical&u

From playlist Physics

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CTNT 2022 - 100 Years of Chebotarev Density (Lecture 3) - by Keith Conrad

This video is part of a mini-course on "100 Years of Chebotarev Density" that was taught during CTNT 2022, the Connecticut Summer School and Conference in Number Theory. More about CTNT: https://ctnt-summer.math.uconn.edu/

From playlist CTNT 2022 - 100 Years of Chebotarev Density (by Keith Conrad)

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CTNT 2022 - 100 Years of Chebotarev Density (Lecture 1) - by Keith Conrad

This video is part of a mini-course on "100 Years of Chebotarev Density" that was taught during CTNT 2022, the Connecticut Summer School and Conference in Number Theory. More about CTNT: https://ctnt-summer.math.uconn.edu/

From playlist CTNT 2022 - 100 Years of Chebotarev Density (by Keith Conrad)

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James Maynard: Half-isolated zeros and zero-density estimates

We introduce a new zero-detecting method which is sensitive to the vertical distribution of zeros of the zeta function. This allows us to show that there are few 'half-isolated' zeros, and allows us to improve the classical zero density result to N(σ,T)≪T24(1−σ)/11+o(1) if we assume that t

From playlist Seminar Series "Harmonic Analysis from the Edge"

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Volume density

Keep going! Check out the next lesson and practice what you’re learning: https://www.khanacademy.org/math/geometry/hs-geo-solids/hs-geo-density/e/surface-and-volume-density-word-problems Volume density is the amount of a quantity (often mass) per unit of volume. Density=Quantity/Volume

From playlist High School Geometry | High School Math | Khan Academy

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Half-Isolated Zeros and Zero-Density Estimates - Kyle Pratt

50 Years of Number Theory and Random Matrix Theory Conference Topic: Half-Isolated Zeros and Zero-Density Estimates Speaker: Kyle Pratt Affiliation: University of Oxford Date: June 23, 2022 We introduce a new zero-detecting method which is sensitive to the vertical distribution of zeros

From playlist Mathematics

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Farzana Nasrin (8/29/21): Random Persistence Diagram Generator

We will discuss in this talk a method of generating random persistence diagrams (RPDG). RPDG is underpinned (i) by a parametric model based on pairwise interacting point processes for inference of persistence diagrams (PDs) and (ii) by a reversible jump Markov chain Monte Carlo (RJ-MCMC) a

From playlist Beyond TDA - Persistent functions and its applications in data sciences, 2021

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Bourbaki - 18/06/2016 - 4/4 - Kannan SOUNDARARAJAN

Kannan SOUNDARARAJAN — The Liouville function in short intervals [after Matomäki and Radziwiłł] The Liouville function λ(n) is a completely multiplicative function, taking the value 1 if n has an even number of prime factors (counted with multiplicity) and −1 if n has an odd number of prim

From playlist Bourbaki - 18 juin 2016

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CTNT 2022 - 100 Years of Chebotarev Density (Lecture 2) - by Keith Conrad

This video is part of a mini-course on "100 Years of Chebotarev Density" that was taught during CTNT 2022, the Connecticut Summer School and Conference in Number Theory. More about CTNT: https://ctnt-summer.math.uconn.edu/

From playlist CTNT 2022 - 100 Years of Chebotarev Density (by Keith Conrad)

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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

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Lecture 16: Fejer’s Theorem and Convergence of Fourier Series

MIT 18.102 Introduction to Functional Analysis, Spring 2021 Instructor: Dr. Casey Rodriguez View the complete course: https://ocw.mit.edu/courses/18-102-introduction-to-functional-analysis-spring-2021/ YouTube Playlist: https://www.youtube.com/watch?v=8IxHMVf3jcA&list=PLUl4u3cNGP63micsJp_

From playlist MIT 18.102 Introduction to Functional Analysis, Spring 2021

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Value distribution of long Dirichlet polynomials and applications to the Riemann...-Maksym Radziwill

Maksym Radziwill Value distribution of long Dirichlet polynomials and applications to the Riemann zeta-function Stanford University; Member, School of Mathematics October 1, 2013 For more videos, visit http://video.ias.edu

From playlist Mathematics

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Henrik Hult: Power-laws and weak convergence of the Kingman coalescent

The Kingman coalescent is a fundamental process in population genetics modelling the ancestry of a sample of individuals backwards in time. In this paper, weak convergence is proved for a sequence of Markov chains consisting of two components related to the Kingman coalescent, under a pare

From playlist Probability and Statistics

Related pages

Dirichlet's theorem on arithmetic progressions | Prime number | L-function | Mathematics | Dirichlet distribution | Prime zeta function | Riemann zeta function | Peter Gustav Lejeune Dirichlet | Natural density