Results 1 to 10 of about 379,338 (251)
A tripling on the algebraic number field [PDF]
Osaka Journal of Mathematics, 1986 Let \(\ell\) be a prime number and let n be a power of \(\ell\). Let k be an algebraic number field of finite degree which contains a primitive n-th root of unity \(\zeta_ n\). In the present paper the author defines a tripling symbol \((x,y,z)_ n\in \), which is defined on a subset of \(k^{\times}\times k^{\times}\times k^{\times}\) consisting of the ...
AKAGAWA, YASUMASA
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On the Units of Algebraic Number Fields
Journal of Number Theory, 1994 Let \(K\) be an algebraic number field of degree \(n\) over the rational number field and \(k\) be a proper subfield of \(K\) with \([K: k]=m\). Further, let \(R_ 1\), \(r_ 1\) denote the number of embeddings of \(K\), \(k\) into the real numbers and \(2R_ 2\), \(2r_ 2\) denote the numbers of embeddings of \(K\), \(k\) into the complex numbers.
Itaru Yamaguchi, H. Takeuchi
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On the units of an algebraic number field [PDF]
Illinois Journal of Mathematics, 1965 James Ax
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On computing the discriminant of an algebraic number field [PDF]
Mathematics of Computation, 1985 Let f ( x ) f(x) be a monic irreducible polynomial in Z [ x ] {\mathbf {Z}}[x] , and r a root of f ( x ) f(x) in C. Let K be the field Q (
Theresa P. Vaughan
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Fuchsian Groups and Algebraic Number Fields [PDF]
Transactions of the American Mathematical Society, 1985 Given the signature of a finitely-generated Fuchsian group, we find the minimal extension of the rationals for which there is a Fuchsian group having the required signature, whose matrix entries lie in this field.
P. L. Waterman, C. Maclachlan
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Sequences of Residues in Algebraic Number Fields
Journal of Number Theory, 1995 Let \(K\) be an algebraic number field of degree \(d\) over the rationals. \(\Lambda_ K(n,m)\) denotes the least positive number such that for almost all prime ideals \(\mathfrak p\) of \(K\) there exists an integer \(\alpha\) and a unit \(u\) in \(K\) with the property that \(\alpha,\alpha + u,\dots,\alpha + (m - 1)u\) are all \(n\)-th power residues \
A.M. Naranjani
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Topological Transcendental Fields
Axioms, 2022 This article initiates the study of topological transcendental fields F which are subfields of the topological field C of all complex numbers such that F only consists of rational numbers and a nonempty set of transcendental numbers. F, with the topology
Taboka Prince Chalebgwa +1 more
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ε-arithmetics for real vectors and linear processing of real vector-valued signals
Journal of Information and Intelligence, 2023 In this paper, we introduce a new concept, namely ε-arithmetics, for real vectors of any fixed dimension. The basic idea is to use vectors of rational values (called rational vectors) to approximate vectors of real values of the same dimension within ε ...
Xiang-Gen Xia
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Prime Spectrum of the Ring of Adeles of a Number Field
Mathematics, 2022 Much is known about the adele ring of an algebraic number field from the perspective of harmonic analysis and class field theory. However, its ring-theoretical aspects are often ignored.
Álvaro Serrano Holgado
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On simple modules with singular highest weights for so2l+1(K) [PDF]
Қарағанды университетінің хабаршысы. Математика сериясы, 2022 In this paper, we study formal characters of simple modules with singular highest weights over classical Lie algebras of type B over an algebraically closed field of characteristic p ≥ h, where h is the Coxeter number. Assume that the highest weights of
Sh.Sh. Ibraev +2 more
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