Related papers: On optimality of mollifiers

A standard task in solid state physics and quantum chemistry is the computation of localized molecular orbitals known as Wannier functions. In this manuscript, we propose a new procedure for computing Wannier functions in one-dimensional…

A quadratic twist of the L-function associated with a modular form is known to satisfy a functional equation, which may be even or odd. A result due to Gross and Zagier explicitly computes the central value of the L-function or its…

One classical measure of the quality of an interpolating function is its Lipschitz constant. In this paper we consider interpolants with additional smoothness requirements, in particular that their derivatives be Lipschitz. We show that…

The three parameters Mittag--Leffler function (often referred as the Prabhakar function) has important applications, mainly in physics of dielectrics, in describing anomalous relaxation of non--Debye type. This paper concerns with the…

We explicitly evaluate a special type of multiple Dirichlet $L$-values at positive integers in two different ways: One approach involves using symmetric functions, while the other involves using a generating function of the values. Equating…

We compute the second moment of spinor $L$-functions at central points of Siegel modular forms on congruence subgroups of large prime level $N$ and give applications to non-vanishing.

Maximally-localized Wannier functions are quantum wavefunctions resembling atomic orbitals that are used to describe electrons in condensed matter. Since their introduction in 1997, these functions have become ubiquitous in ab initio…

This paper is devoted to the semiclassical analysis of the best constants in the magnetic Sobolev embeddings in the case of a bounded domain of the plane carrying Dirichlet conditions. We provide quantitative estimates of these constants…

We consider a mollifying operator with variable step that, in contrast to the standard mollification, is able to preserve the boundary values of functions. We prove boundedness of the operator in all basic Lebesgue, Sobolev and BV spaces as…

The aim of this paper is to give a new proof of the complete characterization of measures for which there exist a solution of the Dirichlet problem for the complex Monge-Ampere operator in the set of plurisubharmonic functions with finite…

We prove a lower bound of the correct order of magnitude in the conductor aspect for small rational moments of Drichlet $L$-functions. Such bounds require new techniques, which is visible from the relationship to non-vanishing results for…

The generalized Stieltjes--Wigert polynomials depending on parameters 0\le p<1 and 0<q<1 are discussed. By removing the mass at zero of the N-extremal solution concentrated in the zeros of the D-function from the Nevanlinna parametrization,…

We study the $2k$-th moment of the family of Dirichlet $L$-functions to a fixed prime modulus on the critical line and establish sharp lower bounds for all real $k \geq 0$ and sharp upper bounds for $k$ in the range $0 \leq k \leq 1$.

We describe algorithms for computing central values of twists of $L$-functions associated to Hilbert modular forms, carry out such computations for a number of examples, and compare the results of these computations to some heuristics and…

The Minkowski question mark function is a rich object which can be explored from the perspective of dynamical systems, complex dynamics, metric number theory, multifractal analysis, transfer operators, integral transforms, and as a function…

Fitting a matrix of a given rank to data in a least squares sense can be done very effectively using 2nd order methods such as Levenberg-Marquardt by explicitly optimizing over a bilinear parameterization of the matrix. In contrast, when…

Discretization of the uniform norm of functions from a given finite dimensional subspace of continuous functions is studied. We pay special attention to the case of trigonometric polynomials with frequencies from an arbitrary finite set…

The standard $L$-functions of $\mathrm{GL}_{2n}$ expressed in terms of the Friedberg-Jacquet global zeta integrals have better structure for arithmetic applications, due to the relation of the linear periods with the modular symbols. The…

In this paper, we propose a new easily implementable method for solving a class of semi-infinite programs, where an approximate linear semidefinite program is constructed for the concerned semi-infinite program based on the duality theory…

In this paper we study the product of two central values of $L$-functions of a twisted modular. We show that it suffices to compute a local polynomial at a finite number of points to decide whether the product is zero. For the proof, we…