Ratios of regulators in totally real extensions of number fields

DOI10.1016/S0022-314X(05)80044-7zbMath0718.11060MaRDI QIDQ2639099

Antone Costa, Eduardo C. Friedman

Publication date: 1991

Published in: Journal of Number Theory (Search for Journal in Brave)

zbMATH Keywords

Salem numbersregulatortotally real number fieldsrelative units

Mathematics Subject Classification ID

Units and factorization (11R27) Algebraic number theory computations (11Y40) Totally real fields (11R80)

Related Items (17)

The relative Hecke integral formula for an arbitrary extension of number fields ⋮ Bounding the $j$-invariant of integral points on $X_{\mathrm {ns}}^{+}(p)$ ⋮ Independent relative units of low height ⋮ Representing algebraic integers as linear combinations of units ⋮ Lower bounds for regulators of number fields in terms of their discriminants ⋮ On Bertrand's and Rodriguez Villegas' higher-dimensional Lehmer conjecture ⋮ Lower bounds for generalized unit regulators ⋮ The arithmetic and geometry of Salem numbers ⋮ A Kronecker limit formula for totally real fields and arithmetic applications ⋮ Ratios of Regulators in Extensions of Number Fields ⋮ Minkowski's theorem on independent conjugate units ⋮ Bounds for discriminants and related estimates for class numbers, regulators and zeros of zeta functions : a survey of recent results ⋮ Covolumes, units, regulator: conjectures by D. Bertrand and F. Rodriguez-Villegas ⋮ Heights, regulators and Schinzel’s determinant inequality ⋮ Solving Thue equations without the full unit group ⋮ Anne-Marie Bergé -- in memoriam (1939--2008) ⋮ Strong spectral gaps for compact quotients of products of \(\text{PSL}(2,\mathbb R)\)

Cites Work

• Salem numbers and L-functions
• An inequality relating the regulator and the discriminant of a number field
• Analytic formulas for the regulator of a number field
• Ideale kleiner Norm in Idealklassen und eine Regulatorabschätzung
• Small Salem numbers
• Eine Regulatorabschätzung
• On a question of Lehmer and the number of irreducible factors of a polynomial
• Notions relatives de régulateurs et de hauteurs
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