Selected Applications of LLL in Number Theory

DOI10.1007/978-3-642-02295-1_7zbMath1241.11001OpenAlexW314193220MaRDI QIDQ5188543

Denis Simon

Publication date: 5 March 2010

Published in: The LLL Algorithm (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/978-3-642-02295-1_7

zbMATH Keywords

LLL algorithmapplications in number theory

Mathematics Subject Classification ID

Number-theoretic algorithms; complexity (11Y16) Research exposition (monographs, survey articles) pertaining to number theory (11-02) Algebraic number theory computations (11Y40)

Related Items (1)

Interactions of computational complexity theory and mathematics

Cites Work

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• Topics in computational algebraic number theory
• On the computation of quadratic 2-class groups
• On Lovász' lattice reduction and the nearest lattice point problem
• Approximation lattices of \(p\)-adic numbers
• A modification of the LLL reduction algorithm
• Factoring polynomials with rational coefficients
• Small solutions of the Legendre equation
• Subexponential algorithms for class group and unit computations
• LLL \(\and\) ABC
• Lattice basis reduction for indefinite forms and an application
• Reduction of Smith normal form transformation matrices
• Polynomial Time Algorithms for Finding Integer Relations among Real Numbers
• Improved Methods for Calculating Vectors of Short Length in a Lattice, Including a Complexity Analysis
• Disproof of the Mertens conjecture.
• Experimental Determination of Apéry-like Identities for ς(2n + 2)
• A Rigorous Subexponential Algorithm For Computation of Class Groups
• The Computational Complexity of Simultaneous Diophantine Approximation Problems
• Polynomial Factorization and Nonrandomness of Bits of Algebraic and Some Transcendental Numbers
• Generalization of the Euclidean algorithm for real numbers to all dimensions higher than two
• Worst-case complexity bounds for algorithms in the theory of integral quadratic forms
• A polynomial reduction algorithm
• Corrigenda
• Analysis of PSLQ, an integer relation finding algorithm
• Empirically Determined Apéry-Like Formulae for ζ(4n+3)
• Extended GCD and Hermite Normal Form Algorithms via Lattice Basis Reduction (addenda and errata)
• Borwein and Bradley's Apérv-Like Formulae for ζ(4n + 3)
• Solving quadratic equations using reduced unimodular quadratic forms
• Closest point search in lattices
• Efficient solution of rational conics
• Advanced Topics in Computional Number Theory
• Knapsack Public Key Cryptosystems and Diophantine Approximation
• LLL: A Tool for Effective Diophantine Approximation
• The van Hoeij Algorithm for Factoring Polynomials
• Algorithmic Number Theory

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