Zobrazeno 1 - 10
of 77
pro vyhledávání: '"P. Adiceam"'
Autor:
Adiceam, Faustin, Shirandami, Victor
The Subspace Theorem due to Schmidt (1972) is a broad generalisation of Roth's Theorem in Diophantine Approximation (1955) which, in the same way as the latter, suffers a notorious lack of effectivity. This problem is tackled from a probabilistic sta
Externí odkaz:
http://arxiv.org/abs/2411.01247
Publikováno v:
Comb. Number Th. 13 (2024) 277-298
The Josephus problem is a well--studied elimination problem consisting in determining the position of the survivor after repeated applications of a deterministic rule removing one person at a time from a given group. A natural probabilistic variant o
Externí odkaz:
http://arxiv.org/abs/2403.18110
Autor:
Adiceam, Faustin, Marmon, Oscar
Given a set of inequalities determined by homogeneous forms, the following intertwined results are established: (1) the volume of the real semi-algebraic domain determined by these inequalities is explicitly determined; it is shown to be related to t
Externí odkaz:
http://arxiv.org/abs/2305.19782
Autor:
Adiceam, Faustin, Marmon, Oscar
We study the density of solutions to Diophantine inequalities involving non-singular ternary forms, or equivalently, the density of rational points close to non-singular plane algebraic curves.
Comment: 31 pages. To appear in Mathematika
Comment: 31 pages. To appear in Mathematika
Externí odkaz:
http://arxiv.org/abs/2204.11607
Autor:
Adiceam, Faustin, Tsokanos, Ioannis
Publikováno v:
Moscow J. Comb. Number Th. 11 (2022) 149-159
A spiral in $\mathbb{R}^{d+1}$ is defined as a set of the form $\left\{\sqrt[d+1]{n}\cdot\boldsymbol{u}_n\right\}_{n\ge 1},$ where $\left(\boldsymbol{u}_n\right)_{n\ge 1}$ is a spherical sequence. Such point sets have been extensively studied, in par
Externí odkaz:
http://arxiv.org/abs/2111.01843
Autor:
Adiceam, Faustin, Tsokanos, Ioannis
A Delone set in $\mathbb{R}^n$ is a set such that (a) the distance between any two of its points is uniformly bounded below by a strictly positive constant and such that (b) the distance from any point to the remaining points in the set is uniformly
Externí odkaz:
http://arxiv.org/abs/2010.06428
Autor:
Adiceam, Faustin
A 1965 problem due to Danzer asks whether there exists a set with finite density in Euclidean space intersecting any convex body of volume one. A suitable weakening of the volume constraint leads to the (much more recent) problem of constructing \emp
Externí odkaz:
http://arxiv.org/abs/2010.06756
Dense forests are discrete subsets of Euclidean space which are uniformly close to all sufficiently long line segments. The degree of density of a dense forest is measured by its visibility function. We show that cut-and-project quasicrystals are nev
Externí odkaz:
http://arxiv.org/abs/1907.03501
The $p$-adic Littlewood Conjecture due to De Mathan and Teuli\'e asserts that for any prime number $p$ and any real number $\alpha$, the equation $$\inf_{|m|\ge 1} |m|\cdot |m|_p\cdot |\langle m\alpha \rangle|\, =\, 0 $$ holds. Here, $|m|$ is the usu
Externí odkaz:
http://arxiv.org/abs/1806.04478
Autor:
Adiceam, Faustin, Zorin, Evgeniy
Let $\Sigma_d^{++}$ be the set of positive definite matrices with determinant 1 in dimension $d\ge 2$. Identifying any two $SL_d(\mathbb{Z})$-congruent elements in $\Sigma_d^{++}$ gives rise to the space of reduced quadratic forms of determinant one,
Externí odkaz:
http://arxiv.org/abs/1607.04467