Related papers: Rational numbers with small denominators in short …

We present a practical algorithm to compute models of rational functions with minimal resultant under conjugation by fractional linear transformations. We also report on a search for rational functions of degrees 2 and 3 with rational…

Analytic combinatorics studies the asymptotic behaviour of sequences through the analytic properties of their generating functions. This article provides effective algorithms required for the study of analytic combinatorics in several…

We prove the existence of secondary terms of order $X^{5/6}$ in the asymptotic formulas for the average size of the genus number of cubic fields and for the number of cubic fields with a given genus number, establishing improved error…

Let $\mathcal{M}\subset \mathbb{R}^n$ be a compact and sufficiently smooth manifold of dimension $d$. Suppose $\mathcal{M}$ is nowhere completely flat. Let $N_{\mathcal{M}}(\delta,Q)$ denote the number of rational vectors $\mathbf{a}/q$…

This paper proposes a new interval-based contractor for nonlinear equations which is minimal when dealing with narrow boxes. The method is based on the centered form classically used by interval algorithms combined with a Gauss Jordan band…

Confidence interval performance is typically assessed in terms of two criteria: coverage probability and interval width (or margin of error). In this paper, we assess the performance of four common proportion interval estimators: the Wald,…

We obtain bounds on estimation error rates for regularization procedures of the form \begin{equation*} \hat f \in {\rm argmin}_{f\in F}\left(\frac{1}{N}\sum_{i=1}^N\left(Y_i-f(X_i)\right)^2+\lambda \Psi(f)\right) \end{equation*} when $\Psi$…

We estimate the number of integer solutions to decomposable form inequalities (both asymptotic estimates and upper bounds are provided) when the degree of the form and the number of variables are relatively prime. These estimates display…

We obtain lower tail estimates for the smallest singular value of random matrices with independent but non-identically distributed entries. Specifically, we consider $n\times n$ matrices with complex entries of the form \[ M = A\circ X + B…

We use a ``weakly formulated'' Sylvester equation $$A^{1/2}TM^{-1/2}-A^{-1/2}TM^{1/2}=F$$ to obtain new bounds for the rotation of spectral subspaces of a nonnegative selfadjoint operator in a Hilbert space. Our bound extends the known…

In this paper, we study how short an interval $[x, x + x^\theta]$ contains an integer of the form $n_1 n_2 n_3$ and $m_1 m_2 m_3 m_4$ with $n_1 \approx n_2 \approx n_3$ and $m_1 \approx m_2 \approx m_3 \approx m_4$. The new idea is to adopt…

This article suggests an efficient class of estimators of population median of the study variable using an auxiliary variable. Asymptotic expressions of bias and mean square error of the proposed class of estimators have been obtained.…

Gross and Smith have put forward generalizations of Hardy - Littlewood twin prime conjectures for algebraic number fields. We estimate the behavior of sums of a singular series that arises in these conjectures, up to lower order terms. More…

We provide a means of computing and estimating the asymptotic distributions of statistics based on an outer minimization of an inner maximization. Such test statistics, which arise frequently in moment models, are of special interest in…

For the problem of high-dimensional sparse linear regression, it is known that an $\ell_0$-based estimator can achieve a $1/n$ "fast" rate on the prediction error without any conditions on the design matrix, whereas in absence of…

In the first part of this short work (in the form of a comment) we add the plots of two more values of the Li-Keiper coefficients lambda5 and lambda6, computed as in our recent work where the first four values were in particular given. This…

Baker, Harman, and Pintz showed that a weak form of the Prime Number Theorem holds in intervals of the form $[x-x^{0.525},x]$ for large $x$. In this paper, we extend a result of Maynard and Tao concerning small gaps between primes to…

So-called functional error estimators provide a valuable tool for reliably estimating the discretization error for a sum of two convex functions. We apply this concept to Tikhonov regularization for the solution of inverse problems for…

Edgeworth-type expansions for convolutions of probability densities and powers of the characteristic functions with non-uniform error terms are established for i.i.d. random variables with finite (fractional) moments of order $s \geq 2$,…

We prove non-trivial bounds for bilinear forms with hyper-Kloosterman sums with characters modulo a prime $q$ which, for both variables of length $M$, are non-trivial as soon as $M\geq q^{3/8+\delta}$ for any $\delta>0$. This range, which…