Results 21 to 30 of about 1,203,239 (192)
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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Relative integral basis for algebraic number fields
International Journal of Mathematics and Mathematical Sciences, 1986 At first conditions are given for existence of a relative integral basis for OK≅Okn−1⊕I with [K;k]=n. Then the constrtiction of the ideal I in OK≅Okn−1⊕I is given for proof of existence of a relative integral basis for OK4(m1,m2)/Ok(m3).
Mohmood Haghighi
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A Topological Perspective on Interacting Algebraic Theories [PDF]
Electronic Proceedings in Theoretical Computer Science, 2017 Techniques from higher categories and higher-dimensional rewriting are becoming increasingly important for understanding the finer, computational properties of higher algebraic theories that arise, among other fields, in quantum computation.
Amar Hadzihasanovic
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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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Units in families of totally complex algebraic number fields
International Journal of Mathematics and Mathematical Sciences, 2004 Multidimensional continued fraction algorithms associated with GLn(ℤk), where ℤk is the ring of integers of an imaginary quadratic field K, are introduced and applied to find systems of fundamental units in families of totally complex algebraic number ...
L. Ya. Vulakh
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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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Character sums in algebraic number fields [PDF]
, 1983 The Pólya-Vinogradov inequality is generalized to arbitrary algebraic number fields K of finite degree over the rationals. The proof makes use of Siegel's summation formula and requires results about Hecke's zeta-functions with Grössencharacters.
Hinz, Jürgen G
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A characterization of half-factorial orders in algebraic number fields [PDF]
arXiv, 2023 We give an algebraic characterization of half-factorial orders in algebraic number fields. This generalizes prior results for seminormal orders and for orders in quadratic number fields.
arxiv
Right triangles with algebraic sides and elliptic curves over number fields [PDF]
, 2009 Given any positive integer n, we prove the existence of infinitely many right triangles with area n and side lengths in certain number fields. This generalizes the famous congruent number problem.
Girondo, Ernesto +4 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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