Related papers: Extension of Estermann's theorem to Euler products…

We establish a higher dimensional counterpart of Bourgain's pointwise ergodic theorem along an arbitrary integer-valued polynomial mapping. We achieve this by proving variational estimates $V_r$ on $L^p$ spaces for all $1<p<\infty$ and…

We prove a doubly exponential bound for the Castelnuovo-Mumford regularity of prime ideals defining varieties with polynomial parametrisation.

We study an infinite countable iteration of the natural product between ordinals. We present an "effective" way to compute this countable natural product, in the non trivial cases the result depends only on the natural sum of the degrees of…

Let X be an algebraic projective variety in {\bf P}^n. Denote by {\cal C}_{\lambda} the space of all effective cycles on X whose homology class is \lambda \in H_{2p} (X,{\bf Z}). It is easy to show that {\cal C}_{\lambda} is an algebraic…

We construct explicit invariant measures for a family of infinite products of random, independent, identically-distributed elements of SL(2,C). The matrices in the product are such that one entry is gamma-distributed along a ray in the…

We consider a product of $2 \times 2$ random matrices which appears in the physics literature in the analysis of some 1D disordered models. These matrices depend on a parameter $\epsilon >0$ and on a positive random variable $Z$. Derrida…

This paper is concerned with the generalized Euler polynomial matrix $\E^{(\alpha)}(x)$ and the Euler matrix $\E$. Taking into account some properties of Euler polynomials and numbers, we deduce product formulae for $\E^{(\alpha)}(x)$ and…

Let $L_n(k)$ denote the least common multiple of $k$ independent random integers uniformly chosen in $\{1,2,\ldots ,n\}$. In this note, using a purely probabilistic approach, we derive a criterion for the convergence in distribution as…

Let $\phi: M\to M$ be a diffeomorphism of a $C^\infty$ compact connected manifold, and $X$ its mapping torus. There is a natural fibration $p:X\to S^1$, denote by $\xi\in H^1(X, \mathbb{Z})$ the corresponding cohomology class. Let…

Heilbronn gave a sufficient condition for a number field with a totally ramified prime to fail to be norm-Euclidean. We say that Heilbronn's criterion applies to a polynomial $f$ if it applies to the number field $K=\mathbb{Q}[x]/(f)$…

We consider the cubic nonlinear Schr\"odinger equation on product manifolds $\mathbb{R}\times \mathbb{T}$. In this paper, we obtain polynomial bounds on the growth in time of high Sobolev norms of the solutions. The main ingredient of the…

In this work we prove a new $L^p$ holomorphic extension result for functions defined on product Lipschitz surfaces with small Lipschitz constants in two complex variables. We define biparameter and partial Cauchy integral operators that…

We provide upper bounds on the density of a symmetric generalized arithmetic progression lacking nonzero elements of the form h(n) for natural numbers n, or h(p) with p prime, for appropriate polynomials h with integer coefficients. The…

Nourdin et al. [9] established the following universality result: if a sequence of off-diagonal homogeneous polynomial forms in i.i.d. standard normal random variables converges in distribution to a normal, then the convergence also holds…

We use some properties of orthogonal polynomials to provide a class of upper/lower variance bounds for a function $g(X)$ of an absolutely continuous random variable $X$, in terms of the derivatives of $g$ up to some order. The new bounds…

The system of $N$ classical particles on the line with the Weierstrass $\wp$ function as potential is known to be completely integrable. Recently D'Hoker and Phong found a beautiful parameterization by the polynomial of degree $N$ of the…

We show that the greatest prime factor of $n^2+h$ is at least $n^{1.312}$ infinitely often. This gives an unconditional proof for the range previously known under the Selberg eigenvalue conjecture. Furthermore, we get uniformity in $h \leq…

A polyhedral product is a natural subspace of a Cartesian product that is specified by a simplicial complex. The modern formalism arose as a generalization of the spaces known as moment-angle complexes which were developed within the…

We say a power series $a_0+a_1q+a_2q^2+\cdots$ is \emph{multiplicative} if $n\mapsto a_n/a_1$ for positive integers $n$ is a multiplicative function. Given the Eisenstein series $E_{2k}(q)$, we consider formal multiplicative power series…

The $n$-grid $E_n$ consists of $n$ equally spaced points in $[-1,1]$ including the endpoints $\pm 1$. The extremal polynomial $p_n^*$ is the polynomial that maximizes the uniform norm $\| p \|_{[-1,1]}$ among polynomials $p$ of degree $\leq…