Elliptic curves | Algebraic number theory

Heegner point

In mathematics, a Heegner point is a point on a modular curve that is the image of a quadratic imaginary point of the upper half-plane. They were defined by Bryan Birch and named after Kurt Heegner, who used similar ideas to prove Gauss's conjecture on imaginary quadratic fields of class number one. (Wikipedia).

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Distance point and plane the Lagrange way

In this video, I derive the formula for the distance between a point and a plane, but this time using Lagrange multipliers. This not only gives us a neater way of solving the problem, but also gives another illustration of the method of Lagrange multipliers. Enjoy! Note: Check out this vi

From playlist Partial Derivatives

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Limit Points

Limit Points In this video, I define the notion of a limit point (also known as a subsequential limit) and give some examples of limit points. Limit points are closed: https://youtu.be/b1jYloJXDYY Check out my Sequences Playlist: https://www.youtube.com/playlist?list=PLJb1qAQIrmmCuFxFs

From playlist Sequences

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Find the midpoint between two points w(–12,–7), T(–8,–4)

👉 Learn how to find the midpoint between two points. The midpoint between two points is the point halfway the line joining two given points in the coordinate plane. To find the midpoint between two points we add the x-coordinates of the two given points and divide the result by 2. This giv

From playlist Points Lines and Planes

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SummerSchool "Arithmetic geometry" Tschinkel - Introduction | 2006

lecture notes: https://drive.google.com/file/d/1VLucSK53-iLrVUbPAanNZ6Lb7nAAgaQ1/view?usp=sharing Clay Mathematics Institute Summer School 2006 on "Arithmetic geometry" survey lectures given at the 2006 Clay Summer School on Arithmetic Geometry at the Mathematics Institute of the Univer

From playlist Clay Mathematics Institute Summer School 2006 on "Arithmetic geometry"

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163 and Ramanujan Constant - Numberphile

Why does Alex Clark, from the University of Leicester, have a strange fascination with 163? More links & stuff in full description below ↓↓↓ Some slightly more advanced stuff in this video, including the Ramanujan Constant and its use in a "famous" April Fool's joke. NUMBERPHILE Website:

From playlist Prime Numbers on Numberphile

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Midpoint of a line segment

Powered by https://www.numerise.com/ Midpoint of a line segment

From playlist Linear sequences & straight lines

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A Tour Of The Lagrange Points. Part 1 - Past And Future Missions To L1

Thanks to gravity, there are places across the Solar System which are nicely balanced. They’re called Lagrange Points and they give us the perfect vantage points for a range of spacecraft missions, from observing the Sun to studying asteroids, and more. Various spacecraft have already vis

From playlist Guide to Space

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Galois Representations 3 by Shaunak Deo

PROGRAM : ELLIPTIC CURVES AND THE SPECIAL VALUES OF L-FUNCTIONS (ONLINE) ORGANIZERS : Ashay Burungale (California Institute of Technology, USA), Haruzo Hida (University of California, Los Angeles, USA), Somnath Jha (IIT - Kanpur, India) and Ye Tian (Chinese Academy of Sciences, China) DA

From playlist Elliptic Curves and the Special Values of L-functions (ONLINE)

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Introduction To Elliptic Curves And Selmer Groups (Part 2) 2 By Sudhanshu Shekhar

PROGRAM : ELLIPTIC CURVES AND THE SPECIAL VALUES OF L-FUNCTIONS (ONLINE) ORGANIZERS : Ashay Burungale (California Institute of Technology, USA), Haruzo Hida (University of California, Los Angeles, USA), Somnath Jha (IIT - Kanpur, India) and Ye Tian (Chinese Academy of Sciences, China) DA

From playlist Elliptic Curves and the Special Values of L-functions (ONLINE)

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Introduction To Elliptic Curves And Selmer Groups (Part 2) 3 by Sudhanshu Shekhar

PROGRAM : ELLIPTIC CURVES AND THE SPECIAL VALUES OF L-FUNCTIONS (ONLINE) ORGANIZERS : Ashay Burungale (California Institute of Technology, USA), Haruzo Hida (University of California, Los Angeles, USA), Somnath Jha (IIT - Kanpur, India) and Ye Tian (Chinese Academy of Sciences, China) DA

From playlist Elliptic Curves and the Special Values of L-functions (ONLINE)

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Daniel Disegni: The p adic Gross Zagier formula on Shimura curves

Abstract: The Gross-Zagier formula relates the heights of Heegner points on elliptic curves over Q to derivatives of L-functions ; together with the work of Kolyvagin, it implies the rank part of the Birch and Swinnerton-Dyer conjecture for curves whose L-function vanishes to order one, as

From playlist HIM Lectures: Junior Trimester Program "Algebraic Geometry"

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Jan Bruinier: Classes of Heegner divisors and traces of singular moduli

Find this video and other talks given by worldwide mathematicians on CIRM's Audiovisual Mathematics Library: http://library.cirm-math.fr. And discover all its functionalities: - Chapter markers and keywords to watch the parts of your choice in the video - Videos enriched with abstracts, b

From playlist SPECIAL 7th European congress of Mathematics Berlin 2016.

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Stark-Heegner cycles for Bianchi modular forms by Guhan Venkat

PERFECTOID SPACES ORGANIZERS: Debargha Banerjee, Denis Benois, Chitrabhanu Chaudhuri, and Narasimha Kumar Cheraku DATE & TIME: 09 September 2019 to 20 September 2019 VENUE: Madhava Lecture Hall, ICTS, Bangalore Scientific committee: Jacques Tilouine (University of Paris, France) Eknath

From playlist Perfectoid Spaces 2019

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What are opposite rays

👉 Learn essential definitions of points, lines, and planes. A point defines a position in space. A line is a set of points. A line can be created by a minimum of two points. A plane is a flat surface made up of at least three points. A plane contains infinite number of lines. A ray is a li

From playlist Points Lines and Planes

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What are opposite rays

👉 Learn essential definitions of points, lines, and planes. A point defines a position in space. A line is a set of points. A line can be created by a minimum of two points. A plane is a flat surface made up of at least three points. A plane contains infinite number of lines. A ray is a li

From playlist Points Lines and Planes

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What are opposite Rays

👉 Learn essential definitions of points, lines, and planes. A point defines a position in space. A line is a set of points. A line can be created by a minimum of two points. A plane is a flat surface made up of at least three points. A plane contains infinite number of lines. A ray is a li

From playlist Points Lines and Planes

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Stark-Heegner points and generalised Kato classes by Henri Darmon

12 December 2016 to 22 December 2016 VENUE : Madhava Lecture Hall, ICTS Bangalore The Birch and Swinnerton-Dyer conjecture is a striking example of conjectures in number theory, specifically in arithmetic geometry, that has abundant numerical evidence but not a complete general solution.

From playlist Theoretical and Computational Aspects of the Birch and Swinnerton-Dyer Conjecture

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Weyl-type hybrid subconvexity ... on shrinking sets - Matthew Young

Matthew Young Texas A & M University; von Neumann Fellow, School of Mathematics November 20, 2014 One of the major themes of the analytic theory of automorphic forms is the connection between equidistribution and subconvexity. An early example of this is the famous result of Duke showing

From playlist Mathematics

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Finding the midpoint between two points

👉 Learn how to find the midpoint between two points. The midpoint between two points is the point halfway the line joining two given points in the coordinate plane. To find the midpoint between two points we add the x-coordinates of the two given points and divide the result by 2. This giv

From playlist Points Lines and Planes

Related pages

Modular curve | Abelian variety | Class number problem | L-function | Upper half-plane | Mathematics | Néron–Tate height | Mordell–Weil group | PARI/GP | Euler system | Rational point