Výsledky vyhledávání

Report

Adelic Rogers' formula and an application

Autor: Alam, Mahbub, Strömbergsson, Andreas

Recently, Seungki Kim proved an extension of Rogers' mean value formula to the adeles of an arbitrary number field. In this paper we give a new proof Kim's formula, and give a criterion ensuring convergence in this formula. We also discuss one applic

Externí odkaz: http://arxiv.org/abs/2401.13476

Zobrazit plný text záznamu

Report

Euclidean lattices: theory and applications

Autor: Fukshansky, Lenny, Hollanti, Camilla

Publikováno v: Communications in Mathematics, Volume 31 (2023), Issue 2 (Special issue: Euclidean lattices: theory and applications) (October 18, 2023) cm:11596

In this editorial survey we introduce the special issue of the journal Communications in Mathematics on the topic in the title of the article. Our main goal is to briefly outline some of the main aspects of this important area at the intersection of

Externí odkaz: http://arxiv.org/abs/2307.08137

Zobrazit plný text záznamu

Report

Accurate and Infinite Prime Prediction from Novel Quasi-Prime Analytical Methodology

Autor: Grant, Robert E., Ghannam, Talal

It is known that prime numbers occupy specific geometrical patterns or moduli when numbers from one to infinity are distributed around polygons having sides that are integer multiple of number 6. In this paper, we will show that not only prime number

Externí odkaz: http://arxiv.org/abs/1903.08570

Zobrazit plný text záznamu

Report

Geometric classification of real ternary octahedral quartics

Autor: Combe, Noémie

Publikováno v: Discrete Computational Geometry, september 2018, vol 60, Issue 2, pp 255-282

Ternary real-valued quartics in $\mathbb{R}^3$ being invariant under octahedral symmetry are considered. The geometric classification of these surfaces is given. A new type of surfaces emerge from this classification.
Comment: 15 pages

Externí odkaz: http://arxiv.org/abs/1410.1300

Zobrazit plný text záznamu

Report

On classifying Minkowskian sublattices

Autor: Keller, Wolfgang, Martinet, Jacques, Schürmann, Achill

Publikováno v: Mathematics of Computation, 81 (2012), 1063-1092

Let $\Lambda$ be a lattice in an $n$-dimensional Euclidean space $E$ and let $\Lambda'$ be a Minkowskian sublattice of $\Lambda$, that is, a sublattice having a basis made of representatives for the Minkowski successive minima of $\Lambda$. We extend

Externí odkaz: http://arxiv.org/abs/0904.3110

Zobrazit plný text záznamu

Report

On the uniform distribution of rational inputs with respect to condition numbers of Numerical Analysis

Autor: Castro, D., Montana, J. L., Pardo, L. M., Martin, J. San

We show that rational data of bounded input length are uniformly distributed with respect to condition numbers of numerical analysis. We deal both with condition numbers of Linear Algebra and with condition numbers for systems of multivariate polynom

Externí odkaz: http://arxiv.org/abs/math/0103093

Zobrazit plný text záznamu

Report

Numerical Approximation of Real Functions and One Minkowski's Conjecture on Diophintine Approximations

Autor: Glazunov, Nikolaj M.

In this paper I consider the applications of several kinds of approximations of real functions to the problem of verified computation (reliable computing) of the range of implicitly defined real function $x_{n+1} = G(x_{1}, ..., x_{n}),$ where depend

Externí odkaz: http://arxiv.org/abs/math/0009057

Zobrazit plný text záznamu

Report

Counting integral matrices with a given characteristic polynomial

Autor: Shah, Nimish A.

Publikováno v: Sankhya Ser. A 62 (2000), no. 3, 386--412 : Special Issue on Ergodic theory and Harmonic analysis, Mumbai (1999).

We give a simpler proof of an earlier result giving an asymptotic estimate for the number of integral matrices, in large balls, with a given monic integral irreducible polynomial as their common characteristic polynomial. The proof uses equidistribut

Externí odkaz: http://arxiv.org/abs/math/0002179

Zobrazit plný text záznamu