Related papers: Quantitative height bounds under splitting conditi…
Given an isotropic quadratic form over a number field which assumes a value $t$, we investigate the distribution of points at which this value is assumed. Building on the previous work about the distribution of small-height zeros of…
In this paper, we investigate the distribution of the maximum of partial sums of certain cubic exponential sums, commonly known as "Birch sums". Our main theorem gives upper and lower bounds (of nearly the same order of magnitude) for the…
We present in this paper a rather general method for the construction of so-called conditionally exactly solvable potentials. This method is based on algebraic tools known from supersymmetric quantum mechanics. Various families of…
We propose a scheme for translating metrological precision bounds into lower bounds on query complexity of quantum search algorithms. Within the scheme the link between quadratic performance enhancement in idealized quantum metrological and…
We give an upper bound for the norm of the determinant of additively indecomposable, totally positive definite quadratic forms defined over the ring of integers of totally real number fields. We apply these results to find lower and upper…
In this paper we consider the problem of counting algebraic numbers $\alpha$ of fixed degree $n$ and bounded height $Q$ such that the derivative of the minimal polynomial $P_{\alpha}(x)$ of $\alpha$ is bounded, $|P_{\alpha}'(\alpha)| <…
Currently, the best upper bounds on the number of rational points on an absolutely irreducible, smooth, projective algebraic curve of genus g defined over a finite field F_q come either from Serre's refinement of the Weil bound if the genus…
Optimal upper and lower error estimates for strong full-discrete numerical approximations of the stochastic heat equation driven by space-time white noise are obtained. In particular, we establish the optimality of strong convergence rates…
This work is concerned with the development of a space-time adaptive numerical method, based on a rigorous a posteriori error bound, for the semilinear heat equation with a general local Lipschitz reaction term whose solution may blow-up in…
Consider the polynomial optimization problem whose objective and constraints are all described by multivariate polynomials. Under some genericity assumptions, %% on these polynomials, we prove that the optimality conditions always hold on…
We consider the semi-classical limit for the Gross-Pitaevskii equation. In order to consider non-trivial boundary conditions at infinity, we work in Zhidkov spaces rather than in Sobolev spaces. For the usual cubic nonlinearity, we obtain a…
Let $F$ be a univariate polynomial or rational fraction of degree $d$ defined over a number field. We give bounds from above on the absolute logarithmic Weil height of $F$ in terms of the heights of its values at small integers: we review…
We give an explicit upper bound for the algebraic degree and an explicit lower bound for the absolute value of the minimum of a polynomial function on a compact connected component of a basic closed semialgebraic set when this minimum is…
In this paper a nonlinear coupled Schrodinger system in the presence of mixed cubic and superlinear power laws is considered. A non standard numerical method is developed to approximate the solutions in higher dimensional case. The idea…
We investigate a variant of Wirsing's problem on approximation to a real number by real algebraic numbers of degree exactly $n$. This has been studied by Bugeaud and Teulie. We improve their bounds for degrees up to $n=7$. Moreover, we…
We establish algebraicity criteria for formal germs of curves in algebraic varieties over number fields and apply them to derive a rationality criterion for formal germs of functions, which extends the classical rationality theorems of…
We give a mathematical structure on an arithmetic surface, that has algebraic meanings over finite places and can estimate the canonical norm for a relative differential form on the arithmetic surface. This will give a lower bound for the…
Building on previous results of Xing, we give new lower bounds on the rate of intersecting codes over large alphabets. The proof is constructive, and uses algebraic geometry, although nothing beyond the basic theory of linear systems on…
The self-destructive percolation model is defined as follows: Consider percolation with parameter $p > p_c$. Remove the infinite occupied cluster. Finally, give each vertex (or, for bond percolation, each edge) that at this stage is vacant,…
Splitting methods constitute a widely used class of numerical integrators for ordinary and partial differential equations, particularly well suited to problems that can be decomposed into simpler subproblems. High-order splitting schemes…