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Algorithmic Number Theory

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Cover of 'Algorithmic Number Theory'

Table of Contents

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    Book Overview
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    Chapter 36 Counting rational points on curves and abelian varieties over finite fields
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    Chapter 37 Computing cubic fields in quasi-linear time
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    Chapter 38 Fast ideal arithmetic via lazy localization
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    Chapter 39 A comparative study of algorithms for computing continued fractions of algebraic numbers
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    Chapter 40 Computing ray class groups, conductors and discriminants
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    Chapter 41 Computing l -isogenies using the p -torsion
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    Chapter 42 On computing Hilbert class fields of prime degree
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    Chapter 43 On the reduction of composed relations from the number field sieve
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    Chapter 44 Checking the $$\mathfrak{p}$$ -adic stark conjecture when $$\mathfrak{p}$$ is archimedean
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    Chapter 45 A multiple polynomial general number field sieve
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    Chapter 46 Construction of high-rank elliptic curves over ℚ and ℚ( t ) with non-trivial 2-torsion
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    Chapter 47 The height on an abelian variety
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    Chapter 48 On lattices over number fields
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    Chapter 49 Minimum discriminants of primitive sextic fields
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    Chapter 50 A new algorithm and refined bounds for extended gcd computation
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    Chapter 51 Application of thue equations to computing power integral bases in algebraic number fields
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    Chapter 52 Computing S -integral points on elliptic curves
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    Chapter 53 Probabilistic computation of the Smith normal form of a sparse integer matrix
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    Chapter 54 Ray class field constructions of curves over finite fields with many rational points
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    Chapter 55 Computing isogenies in $$\mathbb{F}_{2^n } $$
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    Chapter 56 A computational technique for determining relative class numbers of CM-fields
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    Chapter 57 Old and new deterministic factoring algorithms
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    Chapter 58 Efficient algorithms for computing the Jacobi symbol
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    Chapter 59 The number field database on the World Wide web server http://hasse.mathematik.tu-muenchen.de/
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    Chapter 60 An algorithm of subexponential type computing the class group of quadratic orders over principal ideal domains
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    Chapter 61 Computational aspects of Kummer theory
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    Chapter 62 On integral basis reduction in global function fields
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    Chapter 63 Computational aspects of curves of genus at least 2
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    Chapter 64 The complexity of approximate optima for greatest common divisor computations
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    Chapter 65 Compact representation in real quadratic congruence function fields
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    Chapter 66 Discrete logarithms: The effectiveness of the index calculus method
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    Chapter 67 How difficult is it to solve a thue equation?
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    Chapter 68 Elliptic congruence function fields
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    Chapter 69 Algebraic geometry lattices and codes
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    Chapter 70 Computing discrete logarithms with the general number field sieve
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Title
Algorithmic Number Theory
Published by
Springer Berlin Heidelberg, January 2006
DOI 10.1007/3-540-61581-4
ISBNs
978-3-54-061581-1, 978-3-54-070632-8
Editors

Cohen, Henri

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