Elliptic functions | Modular forms
In mathematics, the modular lambda function λ(τ) is a highly symmetric holomorphic function on the complex upper half-plane. It is invariant under the fractional linear action of the congruence group Γ(2), and generates the function field of the corresponding quotient, i.e., it is a Hauptmodul for the modular curve X(2). Over any point τ, its value can be described as a cross ratio of the branch points of a ramified double cover of the projective line by the elliptic curve , where the map is defined as the quotient by the [−1] involution. The q-expansion, where is the nome, is given by: . OEIS: By symmetrizing the lambda function under the canonical action of the symmetric group S3 on X(2), and then normalizing suitably, one obtains a function on the upper half-plane that is invariant under the full modular group , and it is in fact Klein's modular j-invariant. (Wikipedia).
Modular Forms | Modular Forms; Section 1 2
We define modular forms, and borrow an idea from representation theory to construct some examples. My Twitter: https://twitter.com/KristapsBalodi3 Fourier Theory (0:00) Definition of Modular Forms (8:02) In Search of Modularity (11:38) The Eisenstein Series (18:25)
From playlist Modular Forms
LAMBDA Functions: Powerful And Elegant Abstractions
Python’s lambda, a tiny anonymous function, can be useful in a pinch when you’re feeling too lazy to type that extra d-e-f. But did you know that behind this little lambda is actually one of the most powerful & elegant abstractions in the history of computer science? The lambda calculus,
From playlist Functional Programming
Lambda in Python - Advanced Python 08 - Programming Tutorial - Map Filter Reduce
Lambda in Python - Advanced Python 08 - Programming Tutorial - Map Filter Reduce In this Python Advanced Tutorial, we will be learning about Lambda functions in Python. A lambda function is a small (one line) anonymous function that is defined without a name. It is typically used when you
From playlist Advanced Python - Complete Course
Modular Functions | Modular Forms; Section 1.1
In this video we introduce the notion of modular functions. My Twitter: https://twitter.com/KristapsBalodi3 Intro (0:00) Weakly Modular Functions (2:10) Factor of Automorphy (8:58) Checking the Generators (15:04) The Nome Map (16:35) Modular Functions (22:10)
From playlist Modular Forms
This lecture is part of an online graduate course on modular forms. We introduce modular forms, and give several examples of how they were used to solve problems in apparently unrelated areas of mathematics. I will not be following any particular book, but if anyone wants a suggestion
From playlist Modular forms
Python Programming Tutorial - 40 - Lamdba
Source Code: https://github.com/thenewboston-developers Core Deployment Guide (AWS): https://docs.google.com/document/d/16NDHWtmwmsnrACytRXp2T9Jg7R5FgzRmkYoDteFKxyc/edit?usp=sharing
From playlist Python 3.4 Programming Tutorials
Modular forms: Modular functions
This lecture is part of an online graduate course on modular forms. We classify all meromorphic modular functions, showing that they are all rational functions of the elliptic modular function j. As an application of j we use it to prove Picard's theorem that a non-constant meromorphic
From playlist Modular forms
Weakly Modular Functions | The Geometry of SL2,Z, Section 1.4
We provide an alternative motivation for the definition of weakly modular functions. My Twitter: https://twitter.com/KristapsBalodi3 Weakly Modular Functions (0:00) Boring Functions on Compact Riemann Surfaces (2:06) Transforming the Transformation Property (9:15)
From playlist The Geometry of SL(2,Z)
Modular forms: Eisenstein series
This lecture is part of an online graduate course on modular forms. We give two ways of looking at modular forms: as functions of lattices in C, or as invariant forms. We use this to give two different ways of constructing Eisenstein series. For the other lectures in the course see http
From playlist Modular forms
Python Lambda Function | Anonymous Function In Python | Python Tutorial | Edureka
** Python Certification Training: https://www.edureka.co/data-science-python-certification-course ** This Edureka live video on 'Python Lambda' is to educate you about the Lambda functions of Python and help you understand how to use them in various scenarios. Below are the topics cover
From playlist Python Programming Tutorials | Edureka
The standard L-function of Siegel modular forms and applications (Lecture 2) by Ameya Pitale
PROGRAM : ALGEBRAIC AND ANALYTIC ASPECTS OF AUTOMORPHIC FORMS ORGANIZERS : Anilatmaja Aryasomayajula, Venketasubramanian C G, Jurg Kramer, Dipendra Prasad, Anandavardhanan U. K. and Anna von Pippich DATE & TIME : 25 February 2019 to 07 March 2019 VENUE : Madhava Lecture Hall, ICTS Banga
From playlist Algebraic and Analytic Aspects of Automorphic Forms 2019
On the Gross—Stark conjecture 2 by Mahesh Kakde
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)
Maryna Viazovska - 3/6 Automorphic Forms and Optimization in Euclidean Space
Hadamard Lectures 2019 The goal of this lecture course, “Automorphic Forms and Optimization in Euclidean Space”, is to prove the universal optimality of the E8 and Leech lattices. This theorem is the main result of a recent preprint “Universal Optimality of the E8 and Leech Lattices and I
From playlist Hadamard Lectures 2019 - Maryna Viazovska - Automorphic Forms and Optimization in Euclidean Space
Effective height bounds for odd-degree totally real points on some curves - Levent Alpoge
Joint IAS/Princeton University Number Theory Seminar Topic: Effective height bounds for odd-degree totally real points on some curves Speaker: Levent Alpoge Affiliation: Columbia University Date: November 12, 2020 For more video please visit http://video.ias.edu
From playlist Mathematics
DISCUSSION MEETING SPHERE PACKING ORGANIZERS: Mahesh Kakde and E.K. Narayanan DATE: 31 October 2019 to 06 November 2019 VENUE: Madhava Lecture Hall, ICTS Bangalore Sphere packing is a centuries-old problem in geometry, with many connections to other branches of mathematics (number the
From playlist Sphere Packing - 2019
Arithmetic holonomy bounds and Apery limits - Vesselin Dimitrov
Joint IAS/PU Number Theory Seminar Topic: Arithmetic holonomy bounds and Apery limits Speaker: Vesselin Dimitrov Affiliation: Member, School of Mathematics Date: September 22, 2022 A Diophantine upper bound on the dimensions of certain spaces of holonomic functions was the main ingredien
From playlist Mathematics
A Wiles-Diamond numerical criterion in higher dimensions -Chandrashekhar Khare
Joint IAS/Princeton University Number Theory Seminar Topic: A Wiles-Diamond numerical criterion in higher dimensions Speaker: Chandrashekhar Khare Affiliation: University of California, Los Angeles Date: February 17, 2022 Wiles’s proof of the modularity of (semistable) elliptic curves ov
From playlist Mathematics
Chao Li - 2/2 Geometric and Arithmetic Theta Correspondences
Geometric/arithmetic theta correspondences provide correspondences between automorphic forms and cohomology classes/algebraic cycles on Shimura varieties. I will give an introduction focusing on the example of unitary groups and highlight recent advances in the arithmetic theory (also know
From playlist 2022 Summer School on the Langlands program
The LAMBDA Function Explained - How to Create Custom Functions in Excel
Sign up for our Excel webinar, times added weekly: https://www.excelcampus.com/blueprint-registration/ In this video, learn how to create custom functions with the new LAMBDA feature of Excel. This covers everything you need to know to get started, best practices, using LAMBDAS in other wo
From playlist Excel Formulas