Arithmetic functions

Normal order of an arithmetic function

In number theory, a normal order of an arithmetic function is some simpler or better-understood function which "usually" takes the same or closely approximate values. Let f be a function on the natural numbers. We say that g is a normal order of f if for every ε > 0, the inequalities hold for almost all n: that is, if the proportion of n ≤ x for which this does not hold tends to 0 as x tends to infinity. It is conventional to assume that the approximating function g is continuous and monotone. (Wikipedia).

Video thumbnail

Arithmetic Sum

Discrete Math and Arithmetic Sums

From playlist Discrete Math

Video thumbnail

Arithmetic statistics over number fields and function fields - Alexei Entin

Alexei Entin Member, School of Mathematics September 23, 2014 More videos on http://video.ias.edu

From playlist Mathematics

Video thumbnail

Determine Linear Function Values and Express as Ordered Pairs

This video explains how to determine linear function values. Each function value is also expressed as an ordered pair. http://mathispower4u.com

From playlist Determining Function Values

Video thumbnail

Determine if Ordered Pairs Represent a Function and Describe Behavior

This video explains how to determine is a relation given as a set of ordreed pairs is a function and if the function is increasing, decreasing, or constant. http://mathispower4u.com

From playlist Introduction to Functions: Function Basics

Video thumbnail

Function Arithmetic (Quotient): (f*g)(x) and (f*g)(-3) - Long Division

This video explains how to determine the quotient of two functions using long division, not factoring. Then a function value is determined using two methods. http://mathispower4u.com

From playlist The Properties of Functions

Video thumbnail

Ex 2: Determine if a Table Represents a Linear or Exponential Function and Find Equation (Exp)

This video explains how to determine if a table of values represents a linear function or an exponential function. The the equation of the function is determined. http://mathispower4u.com

From playlist Introduction to Exponential Functions

Video thumbnail

Ex 1: Determine if a Table Represents a Linear or Exponential Function and Find Equation (Exp)

This video explains how to determine if a table of values represents a linear function or an exponential function. The the equation of the function is determined. http://mathispower4u.com

From playlist Introduction to Exponential Functions

Video thumbnail

Overview of functions even and odd - Online Tutor - Free Math Videos

👉 Learn how to determine if a function is even or odd. A function is even if the graph of the function is symmetrical about the y-axis, or a function is even if f(x) = f(-x). A function is odd if the graph of the function is symmetrical about the origin, or a function is odd if f(-x) = -f(

From playlist Characteristics of Functions

Video thumbnail

Ex 2: Determine if a Table of Value Represents a Linear or Exponential Function (Fractions/Decimals)

This video explains how to determine if a table of values represents a linear function or an exponential function. http://mathispower4u.com

From playlist Introduction to Exponential Functions

Video thumbnail

Linear equations in smooth numbers - Lilian Matthiesen

Special Year Research Seminar Topic: Linear equations in smooth numbers Speaker: Lilian Matthiesen Affiliation: KTH Royal Institute of Technology Date: October 18, 2022 A number is called y-smooth if all of its prime factors are bounded above by y. The set of y-smooth numbers below x for

From playlist Mathematics

Video thumbnail

Yifeng Liu - Derivative of L-functions for unitary groups (3/3)

In this lecture series, we will focus on the recent advance on the Beilinson-Bloch conjecture for unitary Shimura varieties, more precisely, a Gross-Zagier type formula for automorphic forms on unitary groups of higher ranks. We will start from the general theory of height pairings between

From playlist Franco-Asian Summer School on Arithmetic Geometry (CIRM)

Video thumbnail

Does Infinite Cardinal Arithmetic Resemble Number Theory? - Menachem Kojman

Menachem Kojman Ben-Gurion University of the Negev; Member, School of Mathematics February 28, 2011 I will survey the development of modern infinite cardinal arithmetic, focusing mainly on S. Shelah's algebraic pcf theory, which was developed in the 1990s to provide upper bounds in infinit

From playlist Mathematics

Video thumbnail

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

Video thumbnail

Andrew Sutherland, Arithmetic L-functions and their Sato-Tate distributions

VaNTAGe seminar on April 28, 2020. License: CC-BY-NC-SA Closed captions provided by Jun Bo Lau.

From playlist The Sato-Tate conjecture for abelian varieties

Video thumbnail

G. Freixas i Montplet - Automorphic forms and arithmetic intersections (part 2)

In these lectures I will focus on the Riemann-Roch theorem in Arakelov geometry, in the specific context of some simple Shimura varieties. For suitable data, the cohomological part of the theorem affords an interpretation in terms of both holomorphic and non-holomorphic modular forms. The

From playlist Ecole d'été 2017 - Géométrie d'Arakelov et applications diophantiennes

Video thumbnail

From order to chaos - Pisa, April, 13 - 2018

Centro di Ricerca Matematica Ennio De Giorgi http://crm.sns.it/event/419/ FROM ORDER TO CHAOS - Pisa 2018 Funded by the European Research Council (ERC) under the European Union's Horizon 2020 research and innovation programme (grant agreement N°647133) and partially supported by GNAMPA-I

From playlist Centro di Ricerca Matematica Ennio De Giorgi

Video thumbnail

Python for Data Analysis: Basic Math Operations

This video covers the basic math operators built into Python and the math library, including the modulo operation and rounding functions. This is lesson 2 of a 30-part introduction to the Python programming language for data analysis and predictive modeling. Link to the code notebook belo

From playlist Python for Data Analysis

Video thumbnail

Spectra of metric graphs and crystalline measures - Peter Sarnak

Members' Seminar Topic: Spectra of metric graphs and crystalline measures Speaker: Peter Sarnak Affiliation: Professor, School of Mathematics Date: February 10, 2020 For more video please visit http://video.ias.edu

From playlist Mathematics

Video thumbnail

Ex 1: Determine if a Table of Value Represents a Linear or Exponential Function

This video explains how to determine if a table of values represents a linear function or an exponential function. http://mathispower4u.com

From playlist Introduction to Exponential Functions

Related pages

Hardy–Ramanujan theorem | Monotonic function | Natural number | Average order of an arithmetic function | Almost all | Multiplicity (mathematics) | Continuous function | Extremal orders of an arithmetic function | Number theory | Divisor function