Results 161 to 170 of about 9,944 (204)

Canonicalizing Zeta Generators: Genus Zero and Genus One. [PDF]

Commun Math Phys
Dorigoni D, Doroudiani M, Drewitt J, Hidding M, Kleinschmidt A, Schlotterer O, Schneps L, Verbeek B.   +7 more
europepmc   +1 more source

On the $K(pi, 1)$-property for rings of integers in the mixed case (Algebraic Number Theory and Related Topics 2007)

On the $K(pi, 1)$-property for rings of integers in the mixed case (Algebraic Number Theory and Related Topics 2007)
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Realizability of Two-dimensional Linear Groups over Rings of Integers of Algebraic Number Fields

Algebras and Representation Theory, 2009
This paper is concerned with the following problem. Given the ring of integers \(O_K\) of an algebraic number field \(K\) and a positive integer \(n\), does there exist a finite subgroup \(G\) of \(\mathrm{GL}(n,O_K)\) such that \(O_KG=M(n,O_K)\), where \(O_KG\) is the \(O_K\)-span of \(G\)? In this case \(M(n,O_K)\) is a `Schur ring'.
Dmitry Malinin, Freddy Van Oystaeyen, Van Oystaeyen Freddy   +2 more
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GAUSS AND KLOOSTERMAN SUMS OVER RESIDUE RINGS OF ALGEBRAIC INTEGERS [PDF]

, 2011
Let K be a field of degree n over Q, the field of rational numbers, with ring of integers O. Fix an integer m > 1, say with [Formula: see text] as a product of distinct prime powers, and let χ be a numerical character modulo m of conductor f(χ).
S. Gurak
semanticscholar   +2 more sources

Realizability of Two-dimensional Linear Groups over Rings of Integers of Algebraic Number Fields [PDF]

, 2011
: Given the ring of integers O (K) of an algebraic number field K, for which natural numbers n there exists a finite group G aS,aEuro parts per thousand GL(n, O (K) ) such that O (K) G, the O (K) -span of G, coincides with M(n, O (K) ), the ring of (n x ...
D. Malinin, F. Oystaeyen
semanticscholar   +2 more sources

Prospects for the use of algebraic rings to describe the operation of convolutional neural networks

International Conference on Advances in Artificial Intelligence, 2022
A new type of number systems (integer coding systems) is used. In the system a set of digits, each of which corresponds to a certain prime number, is used instead of digits corresponding to the powers of a certain integer (for example, ten), All the ...
I. Suleimenov, A. Bakirov, Y. Vitulyova
semanticscholar   +1 more source

Ramanujan’s sum in the ring of integers of an algebraic number field

International Journal of Number Theory, 2019
In this paper, we generalize Ramanujan’s sum to the ring of integers of an algebraic number field. We also obtain the orthogonality properties of Ramanujan’s sum in the ring of integers.
Wang, Yujie, Ji, Chungang
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Computing the discrete Fourier transform using residue number systems in a ring of algebraic integers

IEEE Transactions on Information Theory, 1985
A new method is described for computing an \(N=R^ m=2^{vm}\)-point complex discrete Fourier transform that uses quantization within a dense ring of algebraic integers in conjunction with a residue number system over this ring. The algebraic and analytic foundations for the technique are derived and discussed. The architecture for a radix-R fast Fourier
John H. Cozzens, Larry A. Finkelstein
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The ring of integers of an Abelian extension of an algebraic number field as a Galois module

Journal of Soviet Mathematics, 1982
The ringO of integers of a finite Abelian extension K of an algebraic number field k is studied as a module over the group ring Λ=σ[G], where σ is the ring of integers of k and G is the Galois group of K/k. It is proved that the ring σ is a decomposable Λ-module if and only if there exists in K/k an intermediate extension K/F. F≠K, whose degree divides
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