In number theory, a Heegner number (as termed by Conway and Guy) is a square-free positive integer d such that the imaginary quadratic field has class number 1. Equivalently, its ring of integers has unique factorization. The determination of such numbers is a special case of the class number problem, and they underlie several striking results in number theory. According to the (Baker–)Stark–Heegner theorem there are precisely nine Heegner numbers: 1, 2, 3, 7, 11, 19, 43, 67, and 163. (sequence in the OEIS) This result was conjectured by Gauss and proved up to minor flaws by Kurt Heegner in 1952. Alan Baker and Harold Stark independently proved the result in 1966, and Stark further indicated the gap in Heegner's proof was minor. (Wikipedia).
My #MegaFavNumber - The Bremner-Macleod Numbers
Much better video here: https://youtu.be/Ct3lCfgJV_A
From playlist MegaFavNumbers
Conversion Arcs and 2,916,485,648,612,232,232,816 (MegaFavNumbers)
I'm sorry. The MegaFavNumbers playlist: https://www.youtube.com/playlist?list=PLar4u0v66vIodqt3KSZPsYyuULD5meoAo
From playlist MegaFavNumbers
1,010,010,101,000,011 - #MegaFavNumbers
This is my submission to the #megafavnumbers project. My number is 1010010101000011, which is prime in bases 2, 3, 4, 5, 6 and 10. I've open-sourced my code: https://bitbucket.org/Bip901/multibase-primes Clarification: by "ignoring 1" I mean ignoring base 1, since this number cannot be fo
From playlist MegaFavNumbers
My own choice for a number over 1,000,000 is this 617 digit boy: 251959084756578934940271832400483985714292821262040320277771378360436620207075955562640185258807844069182906412495150821892985591491761845028084891200728449926873928072877767359714183472702618963750149718246911650776133798590
From playlist MegaFavNumbers
MegaFavNumbers - A number with 19729 digits
This video is about my MegaFavNumber. It has 19729 digits, and it is a power of two. [This link is now broken, and I can't find it anywhere else. :( ] See all the digits here: https://sites.google.com/site/largenumbers/home/appendix/a/numbers/265536 The OEIS sequence I mentioned: https:/
From playlist MegaFavNumbers
Complex Numbers - Basics | Don't Memorise
Now that we know what imaginary numbers are, we can move on to understanding Complex Numbers. ✅To access all videos related to Complex Numbers, enroll in our full course now: https://infinitylearn.com/microcourses?utm_source=youtube&utm_medium=Soical&utm_campaign=DM&utm_content=bmsapLZM
From playlist Complex Numbers
Encoding with Prime Numbers and Second Ratios - #MegaFavNumbers
It's still Sept 2nd somewhere! I've been fascinated by Prime Numbers and sequences of prime numbers over the last 3 years or so. I've had two sequences approved for inclusion in the oeis.org related to prime numbers, https://oeis.org/A295746 and https://oeis.org/A295973 In this video, ins
From playlist MegaFavNumbers
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
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"
What is Hardy Ramanujan Number? || #YTShorts || Don't Memorise
Ramanujan was fascinated with numbers and made striking contributions to the branch of mathematics. One of which is the Hardy-Ramanujan number. Want to know what this number is? Watch this video- Don’t Memorise brings learning to life through its captivating educational videos. To Know Mo
From playlist Shorts
Maryna Viazovska: CM values of regularized theta lifts
Abstract: In this talk we will discuss arithmetic properties regularized Petersson products between a holomorphic theta series associated to a positive definite binary quadratic form and a weakly holomorphic weight 1 modular form with integral Fourier coefficients. We prove that such a Pet
From playlist HIM Lectures: Junior Trimester Program "Algebraic Geometry"
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"
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)
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)
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)
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
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
Weight Interlacing and Iwasawa Theory by Shilin Lai
PROGRAM ELLIPTIC CURVES AND THE SPECIAL VALUES OF L-FUNCTIONS (HYBRID) ORGANIZERS: Ashay Burungale (CalTech/UT Austin, USA), Haruzo Hida (UCLA), Somnath Jha (IIT Kanpur) and Ye Tian (MCM, CAS) DATE: 08 August 2022 to 19 August 2022 VENUE: Ramanujan Lecture Hall and online The program pla
From playlist ELLIPTIC CURVES AND THE SPECIAL VALUES OF L-FUNCTIONS (2022)
Complex Numbers - Multiplication | Don't Memorise
How are two complex numbers multiplied? Watch this video to know more To access all videos related to Complex Numbers, enrol in our full course now: https://bit.ly/ComplexNumbersDM In this video, we will learn: 0:00 addition of complex numbers 0:27 multiplication of complex numbers To
From playlist Complex Numbers