Results 21 to 30 of about 1,079,946 (348)
A Construction of Rotated Lattices via Totally Real Subfields of the Cyclotomic Field Q(z_p)
Trends in Computational and Applied Mathematics, 2019 The theory of lattices have shown to be useful in information theory and rotated lattices with high modulations diversity have been extensively studied as an alternative approach for transmission over a Rayleigh-fading channel, where the performance of ...
Antonio A. Andrade +2 more
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Formal proofs in real algebraic geometry: from ordered fields to quantifier elimination [PDF]
Logical Methods in Computer Science, 2012 This paper describes a formalization of discrete real closed fields in the Coq proof assistant. This abstract structure captures for instance the theory of real algebraic numbers, a decidable subset of real numbers with good algorithmic properties.
Assia Mahboubi, Cyril Cohen
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Comparing the number of ideals in quadratic number fields
Mathematical Modelling and Control, 2022 Denote by $ a_{K}(n) $ the number of integral ideals in $ K $ with norm $ n $, where $ K $ is a algebraic number field of degree $ m $ over the rational field $ \mathcal{Q} $. Let $ p $ be a prime number.
Qian Wang, Xue Han
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Isomorphisms of algebraic number fields [PDF]
Journal de théorie des nombres de Bordeaux, 2012 Let ℚ(α) and ℚ(β) be algebraic number fields. We describe a new method to find (if they exist) all isomorphisms, ℚ(β)→ℚ(α). The algorithm is particularly efficient if there is only one isomorphism.
van Hoeij, Mark, Pal, Vivek
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Graduate Studies in Mathematics, 1992 Notation Introduction 1. Algebraic foundations 2. Dedekind domains 3. Extensions 4. Classgroups and units 5. Fields of low degree 6. Cyclotomic fields 7. Diophantine equations 8. L-functions Appendices Exercises Glossary of theorems Index.
James S. Milne
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A precise result on the arithmetic of non-principal orders in algebraic number fields [PDF]
, 2011 Let $R$ be an order in an algebraic number field. If $R$ is a principal order, then many explicit results on its arithmetic are available. Among others, $R$ is half-factorial if and only if the class group of $R$ has at most two elements.
Andreas Philipp
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Computation of relative integral bases for algebraic number fields
International Journal of Mathematics and Mathematical Sciences, 1988 At first we are given conditions for existence of relative integral bases for extension (K;k)=n. Then we will construct relative integral bases for extensions OK6(−36)/Ok2(−3), OK6(−36)/Ok3(−33), OK6(−36)/Z.
Mahmood Haghighi
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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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General Quantum Field Theory of Flavor Mixing and Oscillations
Universe, 2021 We review the canonical transformation in quantum physics known as the Bogoliubov transformation and present its application to the general theory of quantum field mixing and oscillations with an arbitrary number of mixed particles with either boson or ...
Chueng-Ryong Ji, Yuriy Mishchenko
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Elementary Fractal Geometry. 2. Carpets Involving Irrational Rotations
Fractal and Fractional, 2022 Self-similar sets with the open set condition, the linear objects of fractal geometry, have been considered mainly for crystallographic data. Here we introduce new symmetry classes in the plane, based on rotation by irrational angles.
Christoph Bandt, Dmitry Mekhontsev
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