Unsolved problems in number theory | Random matrices | Zeta and L-functions | Analytic number theory | Conjectures

Montgomery's pair correlation conjecture

In mathematics, Montgomery's pair correlation conjecture is a conjecture made by Hugh Montgomery that the pair correlation between pairs of zeros of the Riemann zeta function (normalized to have unit average spacing) is which, as Freeman Dyson pointed out to him, is the same as the pair correlation function of random Hermitian matrices. (Wikipedia).

Montgomery's pair correlation conjecture
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SPSS for Beginners 5: Correlations

Updated video: SPSS for Beginners – Correlation https://youtu.be/6EH5DSaCF_8 This video demonstrates how to calculate correlations in SPSS and how to interpret correlation matrices.

From playlist RStats Videos

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Conceptual Questions about Correlation

Please Subscribe here, thank you!!! https://goo.gl/JQ8Nys Conceptual Questions about Correlation

From playlist Statistics

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Pearson's Correlation 1: Correlations and Scatterplots

In this video, I discuss Pearson's Correlation and Scatterplots. Other concepts covered include direction of correlations, the coefficient of determination, and variance shared. Data used for this demonstration is from the CORE2016 project (ID: OER29/15 CCY), the National Institute of Educ

From playlist Pearson Correlation in SPSS

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RELATIONSHIPS Between Variables: Standardized Covariance (7-1)

Correlation is a way of measuring the extent to which two variables are related. The term correlation is synonymous with “relationship.” Variables are related when changes in one variable are consistently associated with changes in another variable. Dr. Daniel reviews Variance, Covariance,

From playlist Correlation And Regression in Statistics (WK 07 - QBA 237)

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Jon Keating: Random matrices, integrability, and number theory - Lecture 2

Abstract: I will give an overview of connections between Random Matrix Theory and Number Theory, in particular connections with the theory of the Riemann zeta-function and zeta functions defined in function fields. I will then discuss recent developments in which integrability plays an imp

From playlist Analysis and its Applications

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Jon Keating: Random matrices, integrability, and number theory - Lecture 3

Abstract: I will give an overview of connections between Random Matrix Theory and Number Theory, in particular connections with the theory of the Riemann zeta-function and zeta functions defined in function fields. I will then discuss recent developments in which integrability plays an imp

From playlist Analysis and its Applications

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Statistics of the Zeros of the Zeta Function: Mesoscopic and Macroscopic Phenomena - Brad Rodgers

Brad Rodgers University of California, Los Angeles March 27, 2013 We review the well known microscopic correspondence between random zeros of the Riemann zeta-function and the eigenvalues of random matrices, and discuss evidence that this correspondence extends to larger mesoscopic collect

From playlist Mathematics

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Random Matrix Theory and Zeta Functions - Peter Sarnak

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From playlist Mathematics

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Opening Remarks and History of the math talks - Peter Sarnak, Hugh Montgomery and Jon Keating

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From playlist Mathematics

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Covariance (8 of 17) What is the Correlation Coefficient?

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From playlist COVARIANCE AND VARIANCE

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Jon Keating: Random matrices, integrability, and number theory - Lecture 4

Abstract: I will give an overview of connections between Random Matrix Theory and Number Theory, in particular connections with the theory of the Riemann zeta-function and zeta functions defined in function fields. I will then discuss recent developments in which integrability plays an imp

From playlist Analysis and its Applications

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Some probabilistic ideas at the interface of random matrix theory and zeta - Ashkan Nikeghbali

Ashkan Nikeghbali UZH April 3, 2014 For more videos, visit http://video.ias.edu

From playlist Mathematics

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Correlation Coefficient

This video explains how to find the correlation coefficient which describes the strength of the linear relationship between two variables x and y. My Website: https://www.video-tutor.net Patreon: https://www.patreon.com/MathScienceTutor Amazon Store: https://www.amazon.com/shop/theorga

From playlist Statistics

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Peter Sarnak "Some analytic applications of the trace formula before and beyond endoscopy" [2012]

2012 FIELDS MEDAL SYMPOSIUM Date: October 17, 2012 11.00am-12.00pm We describe briefly some of the ways in which the trace formula has been used in a non comparative way. In particular we focus on families of automorphic L-functions symmetries associated with them which govern the distrib

From playlist Number Theory

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Intro to the Correlation Coefficient

Brief intro to the correlation coefficient. What it means to have negative correlation, positive correlation or zero correlation. Pearson's, sample and population formulas.

From playlist Correlation

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Emanuel Carneiro: Extremal functions, hilbert spaces, and bounds for the Riemann zeta function

The lecture was held within the framework of the Hausdorff Trimester Program Harmonic Analysis and Partial Differential Equations. 15.7.2014

From playlist HIM Lectures: Trimester Program "Harmonic Analysis and Partial Differential Equations"

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Scatterplots, Part 3: The Formula Behind the Correlation Coefficient

We use the Scatterplots & Correlation app to explain the formula behind the correlation coefficient. The app allows you to find and plot the z-scores, showing the 4 quadrants in which points on the scatterplot can fall.

From playlist Chapter 3: Relationships between two variables

Related pages

Conjecture | Complex number | Interval (mathematics) | Mathematics | Zero of a function | Random matrix | Riemann hypothesis | Correlation function | Fourier transform | Lehmer pair | Riemann zeta function | Hilbert–Pólya conjecture