Related papers: Linear forms of a given Diophantine type and latti…
We propose the use of lattice field theory for the study of string field theory at the non-perturbative quantum level. We identify many potential obstacles and examine possible resolutions thereof. We then experiment with our approach in…
We prove the existence of S-integral solutions of simultaneous diophantine inequalities for pairs (Q,L) involving one quadratic form and one linear form satisfying some arithmetico-geometric conditions. The proof uses strong approximation…
We give a simple proof of a recent inequality by W.M. Schmidt and L. Summerer concerning Diophantine exponents for a linear form in three real variables.
We conjecture recurrence relations satisfied by the degrees of some linearizable lattice equations. This helps to prove linear growth of these equations. We then use these recurrences to search for lattice equations that have linear growth…
In this paper we prove that uniform Diophantine exponents of lattices attain only trivial values.
We define and study structural properties of hypergraphs of models of a theory including lattice ones. Characterizations for the lattice properties of hypergraphs of models of a theory, as well as for structures on sets of isomorphism types…
We prove a generalization of W.M. Schmidt's theorem related to the Diophantine approximations for a linear form of the type $\alpha_1x_1+\alpha_2x_2 +y$ with {\it positive} integers $x_1,x_2$.
The aim of the present paper is to study isomorphisms of canonical ${\cal E}$-lattices. Some interesting results are obtained in the particular case of isomorphisms between two subgroup ${\cal E}$-lattices.
The paper is devoted to the study of the lattice of subgroups of the Lamplighter type groups and to the relative gradient rank.
Zilber's Theorem states that a finite lattice $L$ is planar if{}f it has a complementary order relation. We provide a new proof for this crucial result and discuss some applications, including a canonical form for finite planar lattices and…
We illustrate the use of intersection types as a semantic tool for showing properties of the lattice of lambda theories. Relying on the notion of easy intersection type theory we successfully build a filter model in which the interpretation…
Linear forms in logarithms have an important role in the theory of Diophantine equations. In this article, we prove explicit $p$-adic lower bounds for linear forms in $p$-adic logarithms of rational numbers using Pad\'e approximations of…
In this paper we prove transference inequalities for regular and uniform Diophantine exponents in the weighted setting. Our results generalize the corresponding inequalities that exist in the `non-weighted' case.
This note corrects the paper \cite{ex}, where lattice sequences having exponentially large kissing numbers were constructed. However it was noted in \cite{dif} that the arguments in that paper are not sufficient. Here we correct the…
This paper studies the differential lattice, defined to be a lattice $L$ equipped with a map $d:L\to L$ that satisfies a lattice analog of the Leibniz rule for a derivation. Isomorphic differential lattices are studied and classifications…
We prove a result on linear forms related to Peres-Schlag's theorem on badly approximable numbers with respect to lacunary sequences.
In this paper we introduce the notion of a weak uniform Diophantine exponent of a real number and obtain the complete description of the spectrum of its values.
We study some classes of semi-linear differential equations including both well-posed and ill-posed cases that can generate cocycles (or cocycle correspondences with generating cocycles). Under exponential dichotomy condition with other…
In this paper we study the existence of solutions to an isotropic differential inclusion.
The study of Diophantine triples taking values in linear recurrence sequences is a variant of a problem going back to Diophantus of Alexandria which has been studied quite a lot in the past. The main questions are, as usual, about existence…