Results 261 to 270 of about 11,325,403 (303)

A database for number fields

1996
We describe a database for number fields that has been integrated into the algebraic number theory system Kant. The database gives efficient access to the tables of number fields that have been computed during the last years and is easily extended.
Mario Daberkow, Andreas Weber 0004
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The number fields that are O*-fields II

Quaestiones Mathematicae, 2022
An O* -field is a field K for which each partial order with respect to which K is a partially ordered field can be extended to a total order with respect to which K is a totally ordered field. When F is an even finite-dimensional extension field of ℚ contained in ℝ, necessary and sufficient conditions are ...
Ma, Jingjing, Martinez, Ashley
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Number Fields and Number Rings

1977
A number field is a subfield of ℂ having finite degree (dimension as a vector space) over ℚ. We know (see appendix 2) that every such field has the form ℚ[α] for some algebraic number α ∈ ℂ. If α is a root of an irreducible polynomial over ℚ, having degree n, then $$\mathbb{Q}[\alpha ] = \left\{ {{a_o} + {a_1}\alpha + \cdots + {a_{n - 1}}{\alpha ...
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Definability in number fields

The Journal of Symbolic Logic, 1987
AbstractWe study the sets definable in an algebraic number field by first order formulas of various simple types, showing in particular that N and Z do not have very simple definitions.
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On the Class Numbers of Algebraic Number Fields

Journal of Mathematical Sciences, 2015
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Analysis in the Computable Number Field

Journal of the ACM, 1968
It is well known that real variable analysis is nonconstructive. For example, although it is asserted that every bounded monotone sequence converges to a limit, there is no algorithm for obtaining this limit. This paper presents a constructive analysis which is restricted to a countable set of numbers, the field of computable numbers.
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Discriminants of Number Fields

Jahresbericht der Deutschen Mathematiker-Vereinigung
This paper offers a nice overview on recent research on discriminants of algebraic number fields, especially on lower bounds for the root discriminant. Using (infinite) class field towers, one obtains number fields with small root discriminants. Such fields are needed for lattice-based cryptography, which is important for post-quantum cryptography. The
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Analogies Between Function Fields and Number Fields

American Journal of Mathematics, 1983
Whereas Iwasawa's theory of p-cyclotomic extensions was inspired by Weil's theory of the characteristic polynomial of the Frobenius endomorphism of a function field over a finite field of constants, the authors of the present paper in turn take Iwasawa's theory as a sample for an analogous theory in the setting of function fields resp.
Mazur, B., Wiles, A.
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Modifications to the Number Field Sieve

Journal of Cryptology, 1993
The number field sieve, due to Lenstra et al. and Buhler et al., is a routine for factoring integers. The running time of this algorithm is estimated at \(e^{1.923+ \sigma(1) (\log N)^{1/3} (\log\log N)^{2/3}}\), where \(N\) is the number to be factored and \(\sigma(1)\) tends to 0 as \(N\to\infty\).
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Photocatalysis Enhanced by External Fields

Angewandte Chemie - International Edition, 2021
Tianyi Ma, Yihe Zhang, Hongwei Huang
exaly