Results 41 to 50 of about 387,244 (233)
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.
Waterman, P. L., MacLachlan, C.
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Lower Bounds for Heights in Relative Galois Extensions
, 2017 The goal of this paper is to obtain lower bounds on the height of an algebraic number in a relative setting, extending previous work of Amoroso and Masser.
CJ Smyth +18 more
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MathematicsThe rational field Q is highly desired in many applications. Algorithms using the rational number field Q algebraic number fields use only integer arithmetics and are easy to implement.
Ran Lu
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Another formulation of the Wick’s theorem. Farewell, pairing?
Special Matrices, 2015 The algebraic formulation of Wick’s theorem that allows one to present the vacuum or thermal averages of the chronological product of an arbitrary number of field operators as a determinant (permanent) of the matrix is proposed.
Beloussov Igor V.
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The Square-Zero Basis of Matrix Lie Algebras
Mathematics, 2020 A method is presented that allows one to compute the maximum number of functionally-independent invariant functions under the action of a linear algebraic group as long as its Lie algebra admits a basis of square-zero matrices even on a field of positive
Raúl Durán Díaz +3 more
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On the quantum security of high-dimensional RSA protocol
Journal of Mathematical CryptologyThe idea of extending the classical RSA protocol using algebraic number fields was introduced by Takagi and Naito (Construction of RSA cryptosystem over the algebraic field using ideal theory and investigation of its security.
Rahmani Nour-eddine +3 more
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Helly dimension of algebraic groups
, 2009 It is shown that for a linear algebraic group G over a field of characteristic zero, there is a natural number \kappa(G) such that if a system of Zariski closed cosets in G has empty intersection, then there is a subsystem consisting of at most \kappa(G)
Domokos, M., Szabó, E.
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Algebraic leaves of algebraic foliations over number fields [PDF]
Publications mathématiques de l'IHÉS, 2001 This paper proves an algebraicity criterion for leaves of algebraic foliations over number fields. Let \(K\) be a number field embedded in \(\mathbb C\), let \(X\) be a smooth algebraic variety over \(K\) (i.e., an integral separated scheme of finite type over \(K\)), and let \(F\) be an algebraic subbundle of the tangent bundle \(T_X\). We assume that
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Splitting fields of elements in arithmetic groups
, 2011 We prove that the number of unimodular integral matrices in a norm ball whose characteristic polynomial has Galois group different than the full symmetric group is of strictly lower order of magnitude than the number of all such matrices in the ball, as ...
Gorodnik, Alex, Nevo, Amos
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Splitting full matrix algebras over algebraic number fields
Journal of Algebra, 2012 Let K be an algebraic number field of degree d and discriminant D over Q. Let A be an associative algebra over K given by structure constants such that A is isomorphic to the algebra M_n(K) of n by n matrices over K for some positive integer n. Suppose that d, n and D are bounded.
Ivanyos, Gábor +2 more
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