Results 11 to 20 of about 4,829,005 (281)
Enumerating number fields [PDF]
Annals of Mathematics, 2020 We construct small models of number fields and deduce a better bound for the number of number fields of given degree and bounded discriminant.
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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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Machine-learning number fields
Mathematics, Computation and Geometry of Data, 2022 20 pages, 1 figure, 3 ...
He, Yang-Hui +2 more
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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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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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Ramification in quartic cyclic number fields $K$ generated by $x^4+px^2+p$ [PDF]
Mathematica Bohemica, 2021 If $K$ is the splitting field of the polynomial $f(x)=x^4+px^2+p$ and $p$ is a rational prime of the form $4+n^2$, we give appropriate generators of $K$ to obtain the explicit factorization of the ideal $q{\mathcal O}_K$, where $q$ is a positive rational
Julio Pérez-Hernández +1 more
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, 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.
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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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On dynamical systems induced by p-adic number fields [PDF]
Opuscula Mathematica, 2015 In this paper, we construct dynamical systems induced by \(p\)-adic number fields \(\mathbb{Q}_{p}\). We study the corresponding crossed product operator algebras induced by such dynamical systems.
Ilwoo Cho
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Norms in finite galois extensions of the rationals
International Journal of Mathematics and Mathematical Sciences, 1990 We show that under certain conditions a rational number is a norm in a given finite Galois extension of the rationals if and only if this number is a local norm at a certain finite number of places in a certain finite abelian extension of the rationals.
Hans Opolka
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