Mathematical series | Zeta and L-functions | Series expansions
In mathematics, a Dirichlet series is any series of the form where s is complex, and is a complex sequence. It is a special case of general Dirichlet series. Dirichlet series play a variety of important roles in analytic number theory. The most usually seen definition of the Riemann zeta function is a Dirichlet series, as are the Dirichlet L-functions. It is conjectured that the Selberg class of series obeys the generalized Riemann hypothesis. The series is named in honor of Peter Gustav Lejeune Dirichlet. (Wikipedia).
Bonnie & Clyde: Bonnie, Clyde and the Great Depression | History
Find out how the financial strain of the Great Depression led people to admire Bonnie and Clyde as their tales of bravado in the face of authority offered an escape from a disappointing reality. Subscribe for more Bonnie & Clyde: http://histv.co/SubscribeHistoryYT Love Bonnie & Clyde? F
From playlist Bonnie & Clyde | History
In this video, I define what it means to rearrange (or reshuffle) a series and show that if a series converges absolutely, then any rearrangement of the series converges to the same limit. Interesting Consequence: https://youtu.be/Mw7ocynGVmw Series Playlist: https://www.youtube.com/play
From playlist Series
From playlist Simulink Design Award: 2013 BEST Robotics
This levitron manufactured by my friend İzzet Özgöçmen. We enjoyed playing with it.
From playlist Izzet Özgöçmen
Terrorists Using Drinfeld Modules
This comes from Twenty Four, Season 04, Episode 11
From playlist Mathematical Shenanigans
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
Representation theory: Dirichlet's theorem
In this talk we see how to use characters of finite abelian groups to prove Dirichlet's theorem that there are infinitely many primes in certain arithmetic progressions. We first recall Euler's proof that there are infinitely many primes, which is the simplest case of Dirichlet's proof. T
From playlist Representation theory
Introduction to number theory lecture 49. Dirichlet's theorem
This lecture is part of my Berkeley math 115 course "Introduction to number theory" For the other lectures in the course see https://www.youtube.com/playlist?list=PL8yHsr3EFj53L8sMbzIhhXSAOpuZ1Fov8 We give an overview of the proof of Dirichlet's theorem, and give some examples of Dirichle
From playlist Introduction to number theory (Berkeley Math 115)
Introduction to number theory lecture 45 Dirichlet series
This lecture is part of my Berkeley math 115 course "Introduction to number theory" For the other lectures in the course see https://www.youtube.com/playlist?list=PL8yHsr3EFj53L8sMbzIhhXSAOpuZ1Fov8 We introduce Dirichlet series as generating functions of arithmetical functions and give so
From playlist Introduction to number theory (Berkeley Math 115)
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)
Introduction to number theory lecture 52. Nonvanishing of L series at s=1.
This lecture is part of my Berkeley math 115 course "Introduction to number theory" For the other lectures in the course see https://www.youtube.com/playlist?list=PL8yHsr3EFj53L8sMbzIhhXSAOpuZ1Fov8 We sketch how to show that Dirichlet L functions do not vanish at s=1, completing the proo
From playlist Introduction to number theory (Berkeley Math 115)
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
Introduction to number theory lecture 46. Products of Dirichlet series
This lecture is part of my Berkeley math 115 course "Introduction to number theory" For the other lectures in the course see https://www.youtube.com/playlist?list=PL8yHsr3EFj53L8sMbzIhhXSAOpuZ1Fov8 We discuss products of Dirichlet series and show how to use them to prove identities involv
From playlist Introduction to number theory (Berkeley Math 115)
The Heat Equation: Lecture 4 - Oxford Mathematics 1st Year Student Lecture
The heat equation, also known as the diffusion equation, is central to many areas in applied mathematics. In this series of four lectures - this is the fourth - forming part of the first year undergraduate mathematics course, 'Fourier Series and PDEs', the heat equation is derived and the
From playlist Oxford Mathematics 1st Year Student Lectures: The Heat Equation
Introduction to number theory lecture 50. Dirichlet characters
This lecture is part of my Berkeley math 115 course "Introduction to number theory" For the other lectures in the course see https://www.youtube.com/playlist?list=PL8yHsr3EFj53L8sMbzIhhXSAOpuZ1Fov8 We review some properties of Dirichlet characters in preparation for the proof of Dirichlet
From playlist Introduction to number theory (Berkeley Math 115)