Related papers: G\'en\'eralisations Quantitatives du Crit\'ere D'i…

In 1985, Yu. V. Nesterenko produced a criterion for linear independence, which is a variant of Siegel's. While Siegel uses upper bounds on full systems of forms, Nesterenko uses upper and lower bounds on sufficiently dense sequences of…

In this paper we deduce a lower bound for the rank of a family of $p$ vectors in $\R^k$ (considered as a vector space over the rationals) from the existence of a sequence of linear forms on $\R^p$, with integer coefficients, which are small…

Let $\xi$ be a real irrational number. We are interested in sequences of linear forms in 1 and $\xi$, with integer coefficients, which tend to 0. Does such a sequence exist such that the linear forms are small (with given rate of decrease)…

We consider the problem of simultaneous approximation of real numbers $\theta_1, \ldots,\theta_n$ with rationals and the dual problem of approximating zero with the values of the linear form $x_0+\theta_1x_1+\ldots+\theta_nx_n$ at integer…

In this paper, for a given Dirichlet character mod $N$ with $4\nmid N$, we give a lower bound of order $\sqrt{s/\log(s)}$ for the dimension of the $\mathbb{Q}(e^{2i\pi/N})$-vector space spanned by the values of its $L$-function at integers…

In the restricted setting of product phase space lattices, we give an alternate proof of P. Linnell's theorem on the finite linear independence of lattice Gabor systems in $L^2(\mathbb R^d)$. Our proof is based on a simple argument from the…

In this paper we generalize Nesterenko's criterion to the case where the small linear forms have an oscillating behaviour (for instance given by the saddle point method). This criterion provides both a lower bound for the dimension of the…

We extend Kolchin's results on linear dependence over projective varieties in the constants, to linear dependence over arbitrary complete differential varieties. We show that in this more general setting, the notion of linear dependence…

Finsler's lemma is a classic mathematical result with applications in control and optimization. When the lemma is applied to parameter-dependent LMIs, as such those that arise from problems of robust stability, the extra variables…

We prove a weighted analogue of the Khintchine-Groshev Theorem, where the distance to the nearest integer is replaced by the absolute value. This is subsequently applied to proving the optimality of several linear independence criteria over…

We introduce the notion of $GL(n)$-dependence of matrices, which is a generalization of linear dependence taking into account the matrix structure. Then we prove a theorem, which generalizes, on the one hand, the fact that $n+1$ vectors in…

In this note, we review the latest qualitative results, referring to the Li\'enard Equation, in the framework of non-conformable, generalized and fractional differential operators.

We introduce the notion of dependence, as a property of a Keisler measure, and generalize several results of [HPS13] on generically stable measures (in $NIP$ theories) to arbitrary theories. Among other things, we show that this notion is…

Independence of premise principles play an important role in characterizing the modified realizability and the Dialectica interpretations. In this paper we show that a great many intuitionistic set theories are closed under the…

This paper is complementary to the work Rosen-Silverman, which derives a criteria on the number fields for the independence of Heegner points associated to them on non-CM elliptic curves. We show that the same criteria holds for CM elliptic…

We prove a transcendence theorem concerning values of holomorphic maps from a disk to a quasi-projective variety over $\overline{\mathbf{Q}}$ that are integral curves of some algebraic vector field (defined over $\overline{\mathbf{Q}}$).…

Let $m\ge 2$ be an integer, $K$ an algebraic number field and $\alpha\in K\setminus \{0,-1\}$ with sufficiently small absolute value. In this article, we provide a new lower bound for linear form in…

We study properties of coefficients of a linear form, originating from a multiple integral. As a corollary, we prove Vasilyev's conjecture, connected with the problem of irrationality of the Riemann zeta function at odd integers.

We prove new linear independence results for the values of generalized hypergeometric functions ${}_pF_q$ at several distinct algebraic points, over arbitrary algebraic number fields. Our approach combines constructions of type II Pad\'{e}…

We establish new measures of linear independence of logarithms on commutative algebraic groups in the so-called \emph{rational case}. More precisely, let k be a number field and v_{0} be an arbitrary place of k. Let G be a commutative…