Results 31 to 40 of about 15,143 (166)

Valuations on Structures More General Than Fields

Computer Sciences & Mathematics Forum, 2023
Valuation theory is an important area of investigation in algebra, with applications in algebraic geometry and number theory. In 1957, M. Krasner introduced hyperfields, which are field-like objects with a multivalued addition, to describe some ...
Alessandro Linzi
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The geometry of numbers over algebraic number fields [PDF]

Transactions of the American Mathematical Society, 1958
1. The Geometry of Numbers was founded by Minkowski in order to attack certain arithmetical problems, and is normally concerned with lattices over the rational integers. Minkowski himself, however, also treated a special problem over complex quadratic number fields [5], and a number of writers have since followed him.
Rogers, K., Swinnerton-Dyer, H. P. F.
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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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Computing in the Field of Complex Algebraic Numbers

Journal of Symbolic Computation, 1997
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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On Validated Computing in Algebraic Number Fields

Journal of Symbolic Computation, 1997
The author considers the use of decimal approximations (rather than integer arithmetic) in number field computations required (say) for finding units, e.g., divisibility of two numbers in an order and finding numbers with given norm. The LLL-algorithm is useful in ensuring scaled matrices for the basis (and conjugates).
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The condition number associated with ideal lattices from odd prime degree cyclic number fields

Journal of Mathematical Cryptology
The condition number of a generator matrix of an ideal lattice derived from the ring of integers of an algebraic number field is an important quantity associated with the equivalence between two computational problems in lattice-based cryptography, the ...
de Araujo Robson Ricardo
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On the Tate Conjectures for Divisors on a Fibred Variety and on its Generic Scheme Fibre in the Case of Finite Characteristic

Моделирование и анализ информационных систем, 2017
We investigate interrelations between the Tate conjecture for divisors on a fibred variety over a finite field and the Tate conjecture for divisors on the generic scheme fibre under the condition that the generic scheme fibre has zero irregularity. Let \(
Tatyana V. Prokhorova
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MIXING FOR PROGRESSIONS IN NONABELIAN GROUPS

Forum of Mathematics, Sigma, 2013
We study the mixing properties of progressions $(x, xg, x{g}^{2} )$ , $(x, xg, x{g}^{2} , x{g}^
TERENCE TAO
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On the abc$abc$ conjecture in algebraic number fields

Mathematika, 2023
AbstractIn this paper, we prove a weak form of the conjecture generalised to algebraic number fields. Given integers satisfying , Stewart and Yu were able to give an exponential bound in terms of the radical over the integers (Stewart and Yu [Math. Ann. 291 (1991), 225–230], Stewart and Yu [Duke Math. J. 108 (2001), no. 1, 169–181]), whereas Győry was
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The tree of primes in a field

Cubo, 2010
The product formula of algebraic number theory connects finite and infinite primes in a stringent way, a fact, while not hard to be checked, that has never ceased to be tantalizing.
Wolfgang Rump
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