A fast, rigorous technique for computing the regulator of a real quadratic field

DOI10.1090/S0025-5718-07-01935-7zbMath1126.11072OpenAlexW2031855337MaRDI QIDQ3592698

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Publication date: 13 September 2007

Published in: Mathematics of Computation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/s0025-5718-07-01935-7

zbMATH Keywords

\((fbaby step-giant stepreal quadratic number fieldsp)\) representationsreduced principal idealsregulator computationregulator verification

Mathematics Subject Classification ID

Number-theoretic algorithms; complexity (11Y16) Algebraic number theory computations (11Y40)

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Uses Software

• LiDIA
• NTL

Cites Work

• Subexponential algorithms for class group and unit computations
• An improved real-quadratic-field-based key exchange procedure
• Computer verification of the Ankeny--Artin--Chowla Conjecture for all primes less than $100000000000$
• Über die Berechnung von Klassenzahlen und Klassengruppen algebraischer Zahlkörper.
• A Rigorous Subexponential Algorithm For Computation of Class Groups
• A Numerical Investigation Into the Length of the Period of the Continued Fraction Expansion of √D
• A computational approach for solving $y^2=1^k+2^k+\dotsb+x^k$
• On the Parallel Generation of the Residues for the Continued Fraction Factoring Algorithm
• An Investigation of Bounds for the Regulator of Quadratic Fields
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