Efficient computation of root numbers and class numbers of parametrized families of real abelian number fields

DOI10.1090/S0025-5718-06-01888-6zbMath1109.11065OpenAlexW2099713169MaRDI QIDQ3420441

Stéphane R. Louboutin

Publication date: 2 February 2007

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

Full work available at URL: https://doi.org/10.1090/s0025-5718-06-01888-6

zbMATH Keywords

Gauss sumsclass numbersimplest sextic fieldssimplest cubic fieldssimplest quartic fieldssimplest quintic fields

Mathematics Subject Classification ID

Algebraic number theory computations (11Y40) Cubic and quartic extensions (11R16) Class numbers, class groups, discriminants (11R29) Zeta functions and (L)-functions of number fields (11R42) Other abelian and metabelian extensions (11R20)

Related Items (7)

HT90 and ``simplest number fields ⋮ The second and fourth moments of theta functions at their central point ⋮ On the simplest sextic fields and related Thue equations ⋮ On the Simplest Quartic Fields and Related Thue Equations ⋮ On the order generated by the conjugates of an algebraic integer ⋮ Small Gál sums and applications ⋮ Index, the prime ideal factorization in simplest quartic fields and counting their discriminants

Cites Work

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• Class numbers of cyclotomic fields
• Sums of Gauss, Jacobi, and Jacobsthal
• The simplest quartic fields with ideal class groups of exponents less than or equal to 2
• Simplest cubic fields
• Class numbers and units of E. Lehmer's cyclic quintic fields
• The exponent three class group problem for some real cyclic cubic number fields
• The Calculation of a Large Cubic Class Number with an Application to Real Cyclotomic Fields
• Computation of class numbers of quadratic number fields
• Class Numbers of the Simplest Cubic Fields
• Quintic Polynomials and Real Cyclotomic Fields with Large Class Number
• The determination of Gauss sums
• A Family of Cyclic Quartic Fields Arising from Modular Curves
• Minoration au point 1 des fonctions L et détermination des corps sextiques abéliens totalement imaginaires principaux
• Gaussian Periods and Units in Certain Cyclic Fields
• The Simplest Cubic Fields
• A Computational Technique for Evaluating L(1, χ) and the Class Number of a Real Quadratic Field
• The sextic period polynomial
• Families of irreducible polynomials of Gaussian periods and matrices of cyclotomic numbers
• Computation of relative class numbers of CM-fields by using Hecke $L$-functions
• Special Units in Real Cyclic Sextic Fields
• Class number 3 problem for the simplest cubic fields
• On the class number and unit index of simplest quartic fields

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