Related papers: Distribution modulo one and diophantine approximat…
Let $f : \mathbf{N} \rightarrow \mathbf{C}$ be a bounded multiplicative function. Let $a$ be a fixed integer (say $a = 1$). Then $f$ is well-distributed on the progression $n \equiv a \pmod{q} \subset \{1,\dots, X\}$, for almost all primes…
We give an elementary proof of a recent metrical Diophantine result by D. Kleinbock related to badly approximable vectors in affine subspaces.
We provide a lower bound for the ratio between the ordinary and uniform exponent of both simultaneous Diophantine approximation and Diophantine approximation by linear forms in any dimension. This lower bound was conjectured by Schmidt and…
This text is a slightly expanded version of a survey article on certain aspects of low dimensional dynamics and number theory written after a kind invitation by the editors of the Notices of the American Mathematical Society.
The sole aim of this book is to give a self-contained introduction to concepts and mathematical tools in Bayesian matrix decomposition in order to seamlessly introduce matrix decomposition techniques and their applications in subsequent…
Addendum to the paper Combinatorics of the Modular Group II The Kontsevich integrals, hep-th/9201001, by C. Itzykson and J.-B. Zuber (3 pages)
French translation, by Henri Lombardi and Stefan Neuwirth, of the article "Did Euclid need the Euclidean algorithm to prove unique factorization?", American Mathematical Monthly 113 (2006), pages 196-205.
We prove a new lower bound for the exponent of growth of the best two-dimensional Diophantine approximations with respect to Euclidean norm.
Discussion of "Estimating the Distribution of Dietary Consumption Patterns" by Raymond J. Carroll [arXiv:1405.4667].
We obtain some new inequalities between the ordinary and the uniform Diophantine exponents for simultaneous Diophantine approximation to four real numbers.
Theorems of Khintchine, Groshev, Jarn\'ik, and Besicovitch in Diophantine approximation are fundamental results on the metric properties of $\Psi$-well approximable sets. These foundational results have since been generalised to the…
Theory of $n$-complements with applications is presented.
The aim of this paper is to discuss both higher-order asymptotic expansions and skewed approximations for the Bayesian Discrepancy Measure for testing precise statistical hypotheses. In particular, we derive results on third-order…
In this paper we discuss a general problem on metrical Diophantine approximation associated with a system of linear forms. The main result is a zero-one law that extends one-dimensional results of Cassels and Gallagher. The paper contains a…
This paper is devoted to the study of a problem of Cassels in multiplicative Diophantine approximation which involves minimising values of a product of affine linear forms computed at integral points. It was previously known that values of…
In this chapter we introduce the theory of Diophantine approximation via a series of basic examples from information theory relevant to wireless communications. In particular, we discuss Dirichlet's theorem, badly approximable points,…
In this paper, we consider the problem of counting Diophantine inequalities with multiple natural constraints. We prove a very general result in this setting using dynamical techniques. More precisely, we consider the joint asymptotic…
The main goal of this note is to develop a metrical theory of Diophantine approximation within the framework of the de Mathan-Teulie Conjecture, also known as the `Mixed Littlewood Conjecture'. Let p be a prime. A consequence of our main…
This report is a collection of comments on the Read Paper of Fearnhead and Prangle (2011), to appear in the Journal of the Royal Statistical Society Series B, along with a reply from the authors.
This ia a companion paper to Almost, Lehoczky, Shreve & Yu \cite{ALSY}, where the rationale for studying the diffusion limit of Poisson limit-order book models is explained and the results of a particular "representative" model are…