Results 61 to 70 of about 1,187,035 (128)

Diophantine approximation and filtrations

, 2017
In this talk, I will introduce the notion of height, and how Diophantine inequalities help in Diophantine geometry. Specifically, I'll discuss the theorem of Faltings-Wuestholz and how it uses filtrations to derive Diophantine inequalities.Non ...
McKinnon, David
core   +1 more source

New Hardness Results for Diophantine Approximation [PDF]

We revisit simultaneous diophantine approximation, a classical problem from the geometry of numbers which has many applications in algorithms and complexity. The input of the decision version of this problem consists of a rational vector \alpha, an error
Rothvoß, Thomas, Eisenbrand, Friedrich
core   +2 more sources

Quantitative Khintchine in Simultaneous Approximation

, 2022
In a ground-breaking work \cite{BY}, Beresnevich and Yang recently proved Khintchine's theorem in simultaneous Diophantine approximation for nondegenerate manifolds resolving a long-standing problem in the theory of Diophantine approximation.
Datta, Shreyasi
core  

Diophantine Approximation on a Circle

, 2009
The original problem of Diophantine approximation, which goes back to the famous 1842 theorem of Dirichlet, is that of approximating real numbers by rationals with controlled denominators.
Fukshansky, Lenny
core   +1 more source

Unification of the Nature's Complexities via a Matrix Permanent-Critical Phenomena, Fractals, Quantum Computing, ♯P-Complexity. [PDF]

Entropy (Basel), 2020
Kocharovsky V, Kocharovsky V, Tarasov S.
europepmc   +1 more source

Test sets of the knapsack problem and simultaneous diophantine approximation

, 1997
This paper deals with the study of test sets of the knapsack problem and simultaneous diophantine approximation. The Graver test set of the knapsack problem can be derived from minimal integral solutions of linear diophantine equations.
Weismantel, Robert, Henk, Martin
core   +1 more source

Dynamics on homogeneous spaces and applications to simultaneous diophantine approximation [PDF]

, 2013
We give some new results about diophantine simultaneous inequalities involving one quadratic form and one linear generalising the Oppenheim conjecture. In the first part we compute an exact lower asymptotic estimate of the number of integral values taken
Lazar, Youssef
core   +1 more source

Diophantine exponents of affine subspaces: The simultaneous approximation case

Journal of Number Theory, 2009
We apply nondivergence estimates for flows on homogeneous spaces to compute Diophantine exponents of affine subspaces of $\R^n$ and their nondegenerate submanifolds.
openaire   +2 more sources

Lévy-Khintchin Theorem for best simultaneous Diophantine approximations

Annales Scientifiques de l'École Normale Supérieure
We extend two results about the ordinary continued fraction expansion to best simultaneous Diophantine approximations of vectors or matrices. The first is Levy-Khintchin Theorem about the almost sure growth rate of the denominators of the convergents. The second is a Theorem of Bosma, Hendrik and Wiedijk about the almost sure limit distribution of the ...
Cheung, Yitwah, Chevallier, Nicolas
openaire   +2 more sources

Robust and efficient coding with grid cells. [PDF]

PLoS Comput Biol, 2018
Vágó L, Ujfalussy BB.
europepmc   +1 more source