Results 11 to 20 of about 11,325,403 (303)
, 2023 Number Fields is a textbook for algebraic number theory. It grew out of lecture notes of master courses taught by the author at Radboud University, the Netherlands, over a period of more than four decades. It is self-contained in the sense that it uses only mathematics of a bachelor level, including some Galois theory.
Keune, Frans
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Machine-learning number fields [PDF]
, 2022 We show that standard machine-learning algorithms may be trained to predict certain invariants of algebraic number fields to high accuracy. A random-forest classifier that is trained on finitely many Dedekind zeta coefficients is able to distinguish ...
Oliver, T., He, Y.-H., Lee, K.-H.
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Constructions of Dense Lattices over Number Fields
Trends in Computational and Applied Mathematics, 2020 In this work, we present constructions of algebraic lattices in Euclidean space with optimal center density in dimensions 2,3,4,5,6,8 and 12, which are rotated versions of the lattices Lambda_n, for n =2,3,4,5,6,8 and K_12.
Antonio A. Andrade +3 more
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Universal Chern number statistics in random matrix fields
SciPost Physics, 2023 We investigate the probability distribution of Chern numbers (quantum Hall conductance integers) for a parametric version of the GUE random matrix ensemble, which is a model for a chaotic or disordered system.
Or Swartzberg, Michael Wilkinson, Omri Gat
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Short Principal Ideal Problem in multicubic fields
Journal of Mathematical Cryptology, 2020 One family of candidates to build a post-quantum cryptosystem upon relies on euclidean lattices. In order to make such cryptosystems more efficient, one can consider special lattices with an additional algebraic structure such as ideal lattices.
Lesavourey Andrea +2 more
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Semicircular elements induced by p-adic number fields [PDF]
Opuscula Mathematica, 2017 In this paper, we study semicircular-like elements, and semicircular elements induced by \(p\)-adic analysis, for each prime \(p\). Starting from a \(p\)-adic number field \(\mathbb{Q}_{p}\), we construct a Banach \(*\)-algebra \(\mathfrak{LS}_{p}\), for
Ilwoo Cho, Palle E. T. Jorgensen
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Some Remarks on the Divisibility of the Class Numbers of Imaginary Quadratic Fields
Mathematics, 2022 For a given integer n, we provide some families of imaginary quadratic number fields of the form Q(4q2−pn), whose ideal class group has a subgroup isomorphic to Z/nZ.
Kwang-Seob Kim
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The Genus Field and Genus Number in Algebraic Number Fields [PDF]
Nagoya Mathematical Journal, 1967 Let k be an algebraic number field and K be its normal extension of finite degree. Then the genus field K* of K over k is defined as the maximal unramified extension of K which is obtained from K by composing an abelian extension over k2). We call the degree (K*: K) the genus number of K over k.
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Class Number and Ramification in Number Fields [PDF]
Nagoya Mathematical Journal, 1963 In the ring Ok of algebraic integers of a number field K the group Ik of ideals of Ok modulo the subgroup Pk of principal ideals is a finite abelian group of order hk, the class number of K. The determination of this number is an outstanding problem of algebraic number theory.
Brumer, Armand, Rosen, Michael
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A generalization of arithmetic derivative to p-adic fields and number fields [PDF]
Notes on Number Theory and Discrete MathematicsThe arithmetic derivative is a function from the natural numbers to itself that sends all prime numbers to 1 and satisfies the Leibniz rule. The arithmetic partial derivative with respect to a prime p is the p-th component of the arithmetic derivative ...
Brad Emmons, Xiao Xiao
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