([removed], 9h26) Products of ratios of consecutive integers R´egis de la Bret`eche, Carl Pomerance & G´erald Tenenbaum For Jean-Louis Nicolas, on his sixtieth birthday

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• Sieve theory
• Exponentials
• Exponentiation
• Finite fields
• Information theory
• Jurkat–Richert theorem
• Factorization of polynomials over a finite field and irreducibility tests
• Mathematics
• Abstract algebra
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CHAPTER VI THE HIGHER K-THEORY OF FIELDS The problem of computing the higher K-groups of fields has a rich history, beginning with Quillen’s calculation for finite fields (IV.1.13), and Borel’s calculation of K∗ (

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• Algebraic number theory
• Galois theory
• Homological algebra
• Module theory
• Abelian group
• Algebraic number field
• Finite field
• Torsion
• Divisible group
• Abstract algebra
• Algebra
• Field theory

2014 ARIZONA WINTER SCHOOL: ARITHMETIC STATISTICS STATISTICS FOR ZEROES OF L-FUNCTIONS OF CURVES OVER FINITE FIELDS CHANTAL DAVID The lectures will be concerned with statistics for the zeroes of L-functions in natural fa

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• Algebraic number theory
• Field theory
• Hyperelliptic curve
• Peter Sarnak
• Elliptic curve
• Zeta function
• L-function
• Algebraic number field
• Abstract algebra
• Algebraic curves
• Analytic number theory

CURVES AND ZETA FUNCTIONS OVER FINITE FIELDS POSSIBLE PROJECTS CHANTAL DAVID, CONCORDIA UNIVERSITY ASSISTANT: ALINA BUCUR, UCSD For background material, and more details about the projects, see the notes.

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• Algebra
• Hyperelliptic curve
• Moduli space
• Elliptic curve
• Gonality of an algebraic curve
• Artin–Schreier theory
• L-function
• Zeta function
• Curve
• Abstract algebra
• Algebraic curves
• Geometry

CURVES AND ZETA FUNCTIONS OVER FINITE FIELDS ARIZONA WINTER SCHOOL 2014: ARITHMETIC STATISTICS CHANTAL DAVID ASSISTANT: ALINA BUCUR 1. Introduction

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• Analytic number theory
• Fourier analysis
• Conjectures
• Meromorphic functions
• Riemann hypothesis
• Riemann zeta function
• Elliptic curve
• Dirac delta function
• Algebraic number field
• Mathematical analysis
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Why should anyone have to study mathematics? In Fall 2003, I gave the question above to my Honors Calculus III students. After some lively discussion, they were asked to write a paper on it. The requirements on the pape

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• Coding theory
• XTR
• IP
• Error detection and correction
• Information theory
• Modular arithmetic
• Anatolii Alexeevitch Karatsuba
• Mathematical anxiety
• Mathematics
• Abstract algebra
• Finite fields

Problems for Arizona Winter School 2014: Distribution of discriminants of polynomials over finite fields Jordan S. Ellenberg 1 Feb[removed]In the lectures, we discuss the relationship between questions about probability di

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• Polynomials
• Discriminant
• Monic polynomial
• Finite field
• Resultant
• Étale cohomology
• Factorization of polynomials over a finite field and irreducibility tests
• Algebra
• Abstract algebra
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Reduction of Huge, Sparse Matrices over Finite Fields Via Created Catastrophes Carl Pomerance and J. W. Smith CONTENTS 1. Introduction

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Summer Assignment Math 67 for Math 78 Name __________________________ 1. List the first 5 multiples of 7.

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• Fraction
• Numbers
• Dimensional analysis
• Finite fields
• BCH code
• XTR
• Mathematics
• Division
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ACTA ARITHMETICA[removed]On the smallest pseudopower by

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• Abstract algebra
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• Operator theory
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• Exponential map
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