Results 231 to 240 of about 1,082,587 (269)

On the Class Numbers of Algebraic Number Fields

Journal of Mathematical Sciences, 2015
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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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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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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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Magnetic fields of 30 to 100 kG in the cores of red giant stars

Nature, 2022
Gang Li, Sébastien Deheuvels, J Ballot   +2 more
exaly  

Photocatalysis Enhanced by External Fields

Angewandte Chemie - International Edition, 2021
Shuchen Tu, Na Tian, Tianyi Ma
exaly  

Algebraic Numbers and Number Fields

1998
A number α is called an algebraic number if it satisfies an equation of degree m of the form $${\alpha ^m} + {a_1}{\alpha ^{m - 1}} + {a_2}{\alpha ^{m - 2}} + \cdots + {a_m} = 0$$ where a 1, a 2,..., a m are rational numbers.
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On the Derivations in Number Fields

The Annals of Mathematics, 1951
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Enabling Internal Electric Fields to Enhance Energy and Environmental Catalysis

Advanced Energy Materials, 2023
Jin-Tao Ren, Zhong-Yong Yuan
exaly