An Investigation of Bounds for the Regulator of Quadratic Fields

DOI10.1080/10586458.1995.10504322zbMath0859.11057OpenAlexW2060316621MaRDI QIDQ4891844

Richard F. Lukes, Hugh C. Williams, Michael J. Jacobson jun.

Publication date: 9 April 1997

Published in: Experimental Mathematics (Search for Journal in Brave)

Full work available at URL: https://projecteuclid.org/euclid.em/1062621079

zbMATH Keywords

class numberregulatorquadratic fieldDirichlet \(L\)-functionfundamental unitstatus report

Mathematics Subject Classification ID

Quadratic extensions (11R11) Units and factorization (11R27) Research exposition (monographs, survey articles) pertaining to number theory (11-02) Algebraic number theory computations (11Y40)

Related Items (8)

Well-rounded twists of ideal lattices from real quadratic fields ⋮ Approximating Euler products and class number computation in algebraic function fields ⋮ The Size of the Fundamental Solutions of Consecutive Pell Equations ⋮ A fast, rigorous technique for computing the regulator of a real quadratic field ⋮ Explicit bounds and heuristics on class numbers in hyperelliptic function fields ⋮ A computational approach for solving $y^2=1^k+2^k+\dotsb+x^k$ ⋮ Geometry of biquadratic and cyclic cubic log-unit lattices ⋮ A Conjecture on Units of Quadratic Fields

Cites Work

• A Hochschild homology criterium for the smoothness of an algebra
• The size of \(L(1,\chi)\) for real nonpricipal residue characters \(\chi\) with prime modulus
• Reell-quadratische Zahlkörper mit großer Grundeinheit. (Real- quadratic fields with large fundamental unit)
• Some results on pseudosquares
• On a Titchmarsh-Estermann Sum
• Improvement of a Theorem of Linnik and Walfisz

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