Cyclotomic fields

Quadratic Gauss sum

In number theory, quadratic Gauss sums are certain finite sums of roots of unity. A quadratic Gauss sum can be interpreted as a linear combination of the values of the complex exponential function with coefficients given by a quadratic character; for a general character, one obtains a more general Gauss sum. These objects are named after Carl Friedrich Gauss, who studied them extensively and applied them to quadratic, cubic, and biquadratic reciprocity laws. (Wikipedia).

Video thumbnail

Quadratic App: Find Two Numbers Given Difference and Sum of Squares (Factor)

This video explains how to set up a system of equations and and then solve a quadratic equation to solve an application problem http://mathispower4u.com

From playlist Applications of Quadratic Equations

Video thumbnail

Gaussian Integral 7 Wallis Way

Welcome to the awesome 12-part series on the Gaussian integral. In this series of videos, I calculate the Gaussian integral in 12 different ways. Which method is the best? Watch and find out! In this video, I calculate the Gaussian integral by using a technique that is very similar to the

From playlist Gaussian Integral

Video thumbnail

Quadratic System 2 Algebra Regents

In this video we look at the intersection between and linear and quadratic function

From playlist Quadratic Systems

Video thumbnail

Understanding the discriminant as a part of the quadratic formula

👉 Learn how to solve quadratic equations using the quadratic formula. A quadratic equation is an equation whose highest power on its variable(s) is 2. The quadratic formula is a formula which can be used to find the roots of (solve) a quadratic equation. The quadratic formula is given by

From playlist Solve by Quadratic Formula | x^2+bx+c

Video thumbnail

Theory of numbers: Quadratic reciprocity

This lecture is part of an online undergraduate course on the theory of numbers. We state and law of quadratic reciprocity for Legendre symbols, and prove it using Gauss sums. As applications we show how to use it to calculate Legendre symbols and to test Fermat numbers to see if they are

From playlist Theory of numbers

Video thumbnail

The discriminant and finding the solutions using quadratic formula

👉 Learn how to solve quadratic equations using the quadratic formula. A quadratic equation is an equation whose highest power on its variable(s) is 2. The quadratic formula is a formula which can be used to find the roots of (solve) a quadratic equation. The quadratic formula is given by

From playlist Solve by Quadratic Formula | x^2+bx+c

Video thumbnail

Introduction to number theory lecture 34. Gauss sums

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 define Gauss sums and use them to give another proof of the law of quadratic reciprocity

From playlist Introduction to number theory (Berkeley Math 115)

Video thumbnail

Asymptotics of number fields - Manjul Bhargava [2011]

Asymptotics of number fields Introductory Workshop: Arithmetic Statistics January 31, 2011 - February 04, 2011 January 31, 2011 (11:40 AM PST - 12:40 PM PST) Speaker(s): Manjul Bhargava (Princeton University) Location: MSRI: Simons Auditorium http://www.msri.org/workshops/566

From playlist Number Theory

Video thumbnail

Gaussian Integral 6 Gamma Function

Welcome to the awesome 12-part series on the Gaussian integral. In this series of videos, I calculate the Gaussian integral in 12 different ways. Which method is the best? Watch and find out! In this video, I calculate the Gaussian integral by using properties of the gamma function, which

From playlist Gaussian Integral

Video thumbnail

Mod-01 Lec-14 Convergence of Gaussian Integration

Elementary Numerical Analysis by Prof. Rekha P. Kulkarni,Department of Mathematics,IIT Bombay.For more details on NPTEL visit http://nptel.ac.in

From playlist NPTEL: Elementary Numerical Analysis | CosmoLearning Mathematics

Video thumbnail

Ling Long - Hypergeometric Functions, Character Sums and Applications - Lecture 3

Title: Hypergeometric Functions, Character Sums and Applications Speaker: Prof. Ling Long, Louisiana State University Abstract: Hypergeometric functions form a class of special functions satisfying a lot of symmetries. They are closely related to the arithmetic of one-parameter families of

From playlist Hypergeometric Functions, Character Sums and Applications

Video thumbnail

How to solve a quadratic using the quadratic formula

👉 Learn how to solve quadratic equations using the quadratic formula. A quadratic equation is an equation whose highest power on its variable(s) is 2. The quadratic formula is a formula which can be used to find the roots of (solve) a quadratic equation. The quadratic formula is given by

From playlist Solve by Quadratic Formula | ax^2+bx+c

Video thumbnail

Theory of numbers: Gauss's lemma

This lecture is part of an online undergraduate course on the theory of numbers. We describe Gauss's lemma which gives a useful criterion for whether a number n is a quadratic residue of a prime p. We work it out explicitly for n = -1, 2 and 3, and as an application prove some cases of Di

From playlist Theory of numbers

Video thumbnail

CTNT 2018 - "Arithmetic Statistics" (Lecture 2) by Álvaro Lozano-Robledo

This is lecture 2 of a mini-course on "Arithmetic Statistics", taught by Álvaro Lozano-Robledo, during CTNT 2018, the Connecticut Summer School in Number Theory. For more information about CTNT and other resources and notes, see https://ctnt-summer.math.uconn.edu/

From playlist CTNT 2018 - "Arithmetic Statistics" by Álvaro Lozano-Robledo

Video thumbnail

Number Theory | Quadratic Reciprocity

We prove the quadratic reciprocity theorem. http://www.michael-penn.net http://www.randolphcollege.edu/mathematics/

From playlist Number Theory

Video thumbnail

Quadratic Reciprocity proof -- Number Theory 23

Suggest a problem: https://forms.gle/ea7Pw7HcKePGB4my5 Please Subscribe: https://www.youtube.com/michaelpennmath?sub_confirmation=1 Patreon: https://www.patreon.com/michaelpennmath Merch: https://teespring.com/stores/michael-penn-math Personal Website: http://www.michael-penn.net Randolp

From playlist Number Theory v2

Video thumbnail

Proving Quadratic Reciprocity — Number Theory 23

⭐Support the channel⭐ Patreon: https://www.patreon.com/michaelpennmath Merch: https://teespring.com/stores/michael-penn-math My amazon shop: https://www.amazon.com/shop/michaelpenn ⭐my other channels⭐ Main Channel: https://www.youtube.com/michaelpennmath non-math podcast: http

From playlist Number Theory

Video thumbnail

Ian Petrow (ETH ZĂŒrich) 1/4 - Kloostermania [2017]

notes for this talk: https://www.msri.org/workshops/801/schedules/21768/documents/2985/assets/27967 Introductory Workshop: Analytic Number Theory February 06, 2017 - February 10, 2017 February 06, 2017 (04:45 PM PST - 05:45 PM PST) Speaker(s): Ian Petrow (ETH ZĂŒrich) The Kuznetsov For

From playlist Number Theory

Video thumbnail

Mod-01 Lec-13 Gauss 2-point Rule: Error

Elementary Numerical Analysis by Prof. Rekha P. Kulkarni,Department of Mathematics,IIT Bombay.For more details on NPTEL visit http://nptel.ac.in

From playlist NPTEL: Elementary Numerical Analysis | CosmoLearning Mathematics

Video thumbnail

Factor using the quadratic formula finding real irrational roots

👉 Learn how to solve quadratic equations using the quadratic formula. A quadratic equation is an equation whose highest power on its variable(s) is 2. The quadratic formula is a formula which can be used to find the roots of (solve) a quadratic equation. The quadratic formula is given by

From playlist Solve by Quadratic Formula | ax^2+bx+c

Related pages

Square-free integer | Chinese remainder theorem | Multiplicative function | Kummer sum | Proofs of quadratic reciprocity | Carl Friedrich Gauss | Jacobi symbol | Greatest common divisor | Exponential function | Cyclotomic field | Peter Gustav Lejeune Dirichlet | Quadratic reciprocity | Gauss sum | Landsberg–Schaar relation | Cubic reciprocity | Number theory | Leopold Kronecker | Prime number | Issai Schur | Algebraic integer | Hensel's lemma | Gaussian period | Completing the square