Equidistribution in Number Theory, An Introduction (Record no. 61266)

MARC details
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fixed length control field 06060nam a22005295i 4500
001 - CONTROL NUMBER
control field 978-1-4020-5404-4
003 - CONTROL NUMBER IDENTIFIER
control field DE-He213
005 - DATE AND TIME OF LATEST TRANSACTION
control field 20251006084521.0
007 - PHYSICAL DESCRIPTION FIXED FIELD--GENERAL INFORMATION
fixed length control field cr nn 008mamaa
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fixed length control field 100301s2007 ne | s |||| 0|eng d
020 ## - INTERNATIONAL STANDARD BOOK NUMBER
International Standard Book Number 9781402054044
020 ## - INTERNATIONAL STANDARD BOOK NUMBER
International Standard Book Number 99781402054044
024 7# - OTHER STANDARD IDENTIFIER
Standard number or code 10.1007/978-1-4020-5404-4
Source of number or code doi
082 04 - DEWEY DECIMAL CLASSIFICATION NUMBER
Classification number 512.7
Edition information 23
100 1# - MAIN ENTRY--PERSONAL NAME
Personal name Granville, Andrew.
Relator term editor.
245 10 - TITLE STATEMENT
Title Equidistribution in Number Theory, An Introduction
Medium [electronic resource] /
Statement of responsibility, etc. edited by Andrew Granville, Zeév Rudnick.
246 3# - VARYING FORM OF TITLE
Title proper/short title Proceedings of the NATO Advanced Study Institute on Equidistribution in Number Theory, Montreal, Canada, 11-22 July 2005
264 #1 - PRODUCTION, PUBLICATION, DISTRIBUTION, MANUFACTURE, AND COPYRIGHT NOTICE
Place of production, publication, distribution, manufacture Dordrecht :
Name of producer, publisher, distributor, manufacturer Springer Netherlands,
Date of production, publication, distribution, manufacture, or copyright notice 2007.
300 ## - PHYSICAL DESCRIPTION
Extent XV, 345 p.
Other physical details online resource.
336 ## - CONTENT TYPE
Content type term text
Content type code txt
Source rdacontent
337 ## - MEDIA TYPE
Media type term computer
Media type code c
Source rdamedia
338 ## - CARRIER TYPE
Carrier type term online resource
Carrier type code cr
Source rdacarrier
347 ## - DIGITAL FILE CHARACTERISTICS
File type text file
Encoding format PDF
Source rda
490 1# - SERIES STATEMENT
Series statement NATO Science Series,
International Standard Serial Number 1568-2609 ;
Volume/sequential designation 237
505 0# - FORMATTED CONTENTS NOTE
Formatted contents note Preface. Contributors -- Biographical Sketches of the Lecturers. Uniform Distribution -- 1. Uniform Distribution mod One.2. Fractional Parts of an2 .3. Uniform Distribution mod N.4. Normal Numbers. Sieving and the Erdos-Kac Theorem -- Uniform Distribution, Exponential Sums, and Cryptography -- 1 Randomness and Pseudorandomness. 2 Uniform Distribution and Exponential Sums. 3. Exponential Sums and Cryptography. 4. Some Exponential Sum Bounds. 5. General Modulus and Discrepancy of Diffie-Hellman Triples. 6. Pseudorandom Number Generation. 7 Large Periods and the Carmichael Function. 8 Exponential Sums to General Modulus. 9. Sums over Elliptic Curves. 10 Proof Sketch of Theorem 4.1. The Distribution of Prime Numbers -- 1. The Cramer Model and Gaps Between Consecutive Primes. 2 The Distribution of Primes in Longer Intervals. 3 Maier's Method and an "Uncertainty Principle" -- Torsion Points on Curves -- 1. Introduction. 2. A Proof Using Galois Theory. 3. Polynomials Vanishing at Roots of Unity. The distribution of roots of a polynomial -- 1. Introduction. 2 Algebraic Numbers. 3 In k Dimensions: the Bilu Equidistribution Theorem. 4. Lower Bounds on Heights. 5. Compact Sets with Minimal Energy -- Manin-Mumford, André-Oort, the Equidistribution Point of View -- 1 Introduction.2 Informal Examples of Equi-Distribution.3. The Manin-Mumford and the André-Oort Conjecture. 4. Equidistribution of Special Subvarieties; Analytic Methods for the Distribution of Rational Points on Algebraic Varieties -- 1. Introduction to the Hardy-Littlewood Circle Method. 2. Major Arcs and Local Factors in the Hardy-Littlewood Circle Method. 3. The Minor Arcs in the Hardy-Littlewood Circle Method.4. Combining Analytic and Geometric Methods. Universal Torsors over Del Pezzo Surfaces and Rational Points -- 1. Introduction. 2. Geometric Background. 3. Manin's Conjecture. 4. The Universal Torsor. 5. Summations.6. Completion of the Proof. 7. Equations of Universal Torsors -- An Introduction to the Linnik Problems -- 1. Introduction.2. The Linnik Problems. 3. Holomorphic Modular Forms of Half-Integral Weight. 4. Theta Series With Harmonic Polynomials. 5. Linnik Problem for Squares and the Shimura Lift. 6. Nontrivial Estimates for Fourier Coefficients.7. Salié Sums. 8. An Estimate of Iwaniec. 9. Theorems of Gauss and Siegel . 10. The Nonholomorphic Case (Duke, 1988). 11. Transition to Subconvexity Bounds for L-Functions. 12. An Application to Traces of Singular Moduli. Distribution Modulo One and Ratner's Theorem -- 1. Introduction. 2. Randomness of Point Sequences mod 1. 3. ma mod One 4. vma mod One.5. Ratner's Theorem. Spectral Theory of Automorphic Forms: A Very Brief Introduction -- 1. What Is a Homogeneous Space?. 2. Spectral Theory: Compact Case. 3. Dynamics. 4. Spectral Theory: Noncompact Case. 5. Hecke Operators. 6. Gross Omissions: The Selberg Trace Formula. Some Examples How to Use Measure Classification in Number Theory -- 1. Introduction. 2. Dynamical Systems: Some Background. 3. Equidistribution of n2a mod 1. 4. Unipotent Flows and Ratner's Theorems. 5. Entropy of Dynamical Systems: Some More Background. 6. Diagonalizable Actions and the Set of Exceptions to Littlewood's Conjecture. 7. Applications to Quantum Unique Ergodicity.-An Introduction to Quantum Equidistribution -- 1. Introduction. 2. A Crash Course in Classical Mechanics. 3.A Crash Course in Quantum Mechanics. 4. Two Words on Semi-Classical Analysis. 5. Quantum Mechanics on the Torus. The Arithmetic Theory of Quantum Maps -- 1. Quantum Mechanics on the Torus. 2. Quantizing Cat Maps. 3. Quantum Ergodicity. 4. Quantum Unique Ergodicity. 5. Arithmetic QUE.
520 ## - SUMMARY, ETC.
Summary, etc. Written for graduate students and researchers alike, this set of lectures provides a structured introduction to the concept of equidistribution in number theory. This concept is of growing importance in many areas, including cryptography, zeros of L-functions, Heegner points, prime number theory, the theory of quadratic forms, and the arithmetic aspects of quantum chaos. The volume brings together leading researchers from a range of fields, whose accessible presentations reveal fascinating links between seemingly disparate areas.
650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM
Topical term or geographic name entry element MATHEMATICS.
650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM
Topical term or geographic name entry element GEOMETRY, ALGEBRAIC.
650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM
Topical term or geographic name entry element DIFFERENTIABLE DYNAMICAL SYSTEMS.
650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM
Topical term or geographic name entry element FOURIER ANALYSIS.
650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM
Topical term or geographic name entry element NUMBER THEORY.
650 14 - SUBJECT ADDED ENTRY--TOPICAL TERM
Topical term or geographic name entry element MATHEMATICS.
650 24 - SUBJECT ADDED ENTRY--TOPICAL TERM
Topical term or geographic name entry element NUMBER THEORY.
650 24 - SUBJECT ADDED ENTRY--TOPICAL TERM
Topical term or geographic name entry element ALGEBRAIC GEOMETRY.
650 24 - SUBJECT ADDED ENTRY--TOPICAL TERM
Topical term or geographic name entry element DYNAMICAL SYSTEMS AND ERGODIC THEORY.
650 24 - SUBJECT ADDED ENTRY--TOPICAL TERM
Topical term or geographic name entry element MEASURE AND INTEGRATION.
650 24 - SUBJECT ADDED ENTRY--TOPICAL TERM
Topical term or geographic name entry element FOURIER ANALYSIS.
700 1# - ADDED ENTRY--PERSONAL NAME
Personal name Rudnick, Zeév.
Relator term editor.
710 2# - ADDED ENTRY--CORPORATE NAME
Corporate name or jurisdiction name as entry element SpringerLink (Online service)
773 0# - HOST ITEM ENTRY
Title Springer eBooks
776 08 - ADDITIONAL PHYSICAL FORM ENTRY
Relationship information Printed edition:
International Standard Book Number 9781402054020
830 #0 - SERIES ADDED ENTRY--UNIFORM TITLE
Uniform title NATO Science Series,
International Standard Serial Number 1568-2609 ;
Volume/sequential designation 237
856 40 - ELECTRONIC LOCATION AND ACCESS
Uniform Resource Identifier <a href="http://dx.doi.org/10.1007/978-1-4020-5404-4">http://dx.doi.org/10.1007/978-1-4020-5404-4</a>
Public note Ver el texto completo en las instalaciones del CICY
912 ## -
-- ZDB-2-SMA
942 ## - ADDED ENTRY ELEMENTS (KOHA)
Source of classification or shelving scheme Dewey Decimal Classification
Koha item type Libros electrónicos
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Lost status Source of classification or shelving scheme Damaged status Not for loan Collection Home library Current library Shelving location Date acquired Total checkouts Full call number Date last seen Price effective from Koha item type
  Dewey Decimal Classification     Libro electrónico CICY CICY Libro electrónico 06.10.2025   512.7 06.10.2025 06.10.2025 Libros electrónicos