Algorithmic Number Theory

Table of Contents

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   Book Overview
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   Chapter 36 On the difficulty of finding reliable witnesses
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   Chapter 37 Density computations for real quadratic 2-class groups
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   Chapter 38 Lattice sieving and trial division
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   Chapter 39 A subexponential algorithm for discrete logarithms over the rational subgroup of the Jacobians of large genus hyperelliptic curves over finite fields
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   Chapter 40 Computing rates of growth of division fields on CM Abelian varieties
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   Chapter 41 Algorithms for CM-Fields
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   Chapter 42 Schoof's algorithm and isogeny cycles
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   Chapter 43 Integer points on rational elliptic curves
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    Chapter 44 Counting the number of points on elliptic curves over finite fields of characteristic greater than three
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    Chapter 45 Straight-line complexity and integer factorization
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    Chapter 46 Decomposition of algebraic functions
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    Chapter 47 A new modular interpolation algorithm for factoring multivariate polynomials
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    Chapter 48 The function field sieve
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    Chapter 49 Heegner point computations
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    Chapter 50 Computing the degree of a modular parametrization
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    Chapter 51 Galois representations from the cohomology of SL(3,ℤ)
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    Chapter 52 An analysis of the Gaussian algorithm for lattice reduction
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    Chapter 53 A fast variant of the Gaussian reduction algorithm
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    Chapter 54 Reducing lattice bases by means of approximations
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    Chapter 55 Analysis of a left-shift binary GCD algorithm
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    Chapter 56 The complexity of greatest common divisor computations
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    Chapter 57 Explicit formulas for units in certain quadratic number fields
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    Chapter 58 Factorization of polynomials over finite fields in subexponential time under GRH
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    Chapter 59 On orders of optimal normal basis generators
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    Chapter 60 Computing in the jacobian of a plane algebraic curve
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    Chapter 61 Under the assumption of the Generalized Riemann Hypothesis verifying the class number belongs to NP ∩ co-NP
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    Chapter 62 Calculating the class number of certain Hilbert class fields
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    Chapter 63 Efficient checking of computations in number theory
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    Chapter 64 Constructing elliptic curves with given group order over large finite fields
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    Chapter 65 Computing π(x), M(x) and Ψ(x)
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    Chapter 66 On some applications of finitely generated semi-groups
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    Chapter 67 Improved incremental prime number sieves
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    Chapter 68 Polynomial time algorithms for discrete logarithms and factoring on a quantum computer
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    Chapter 69 On dispersion and Markov constants
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    Chapter 70 Open problems in number theoretic complexity, II