Related papers: Integrating Singular Functions on the Sphere
We study integral points on affine surfaces by means of a new method, relying on the Subspace Theorem. Under suitable assumptions on the divisor at infinity, we prove that the integral points are contained in a curve. As a corollary, we…
We show that the standard boundary integral operators, defined on the unit sphere, for the Stokes equations diagonalize on a specific set of vector spherical harmonics and provide formulas for their spectra. We also derive analytical…
In this paper, we employ contour integration and residue calculus to derive explicit parity formulas for (cyclotomic) multiple zeta values (MZVs). A key innovation lies in applying double shuffle regularization to the contour integrals,…
Functions with singularities are notoriously difficult to approximate with conventional approximation schemes. In computational applications, they are often resolved with low-order piecewise polynomials, multilevel schemes, or other types…
We develop a duality for operations on nested pairs of modules that generalizes the duality between absolute interior operations and residual closure operations from [ER21], extending our previous results to the expanded context. We apply…
We supplement the result of the first part of the work with estimates of the integrals of the difference of subharmonic functions in measure with some deterioration of the absolute constants, but these estimates have the form of a…
We give a new method for the evaluation of a class of integrals of rational symmetric functions in N pairs of variables {x_a, y_a}_{a=1,... N} arising in coupled matrix models, valid for a broad class of two-variable measures. The result is…
We compute the integral of monomials of the form $x^{2\beta}$ over the unit sphere and the unit ball in $R^n$ where $\beta = (\beta_1,...,\beta_n)$ is a multi-index with real components $\beta_k > -1/2$, $1 \le k \le n$, and discuss their…
It is well known that for a first order system of linear difference equations with rational function coefficients, a solution that is holomorphic in some left half plane can be analytically continued to a meromorphic solution in the whole…
We introduce fractional integrals on the $n$-dimensional spherical cap, study their boundednes in weighted $L^p$ spaces and obtain explicit inversion formulas. The results are applied to the inversion problem for Riesz potentials on a…
Contour integration is a crucial technique in many numeric methods of interest in physics ranging from differentiation to evaluating functions of matrices. It is often important to determine whether a given contour contains any poles or…
We show how the sine and cosine integrals may be usefully employed in the evaluation of some more complex integrals.
We investigate the count of meromorphic differentials on the Riemann sphere possessing a single zero, multiple poles with prescribed orders, and fixed residues at each pole. Gendron and Tahar previously examined this problem with respect to…
In this work we blend interpolation theory with numerical integration, constructing an interpolator based on integrals over $n$-dimensional balls. We show that, under hypotheses on the radius of the $n$-balls, the problem can be treated as…
This article is the second of a series of three presenting an alternative method to compute the one-loop scalar integrals. It extends the results of the first article to general complex masses. Let us remind the main features enjoyed by…
We derive an analytic expression for the scalar one-loop pentagon and hexagon functions which is convenient for subsequent numerical integration. These functions are of relevance in the computation of next-to-leading order radiative…
An efficient evaluation method is described for polynomials in finite fields. Its complexity is shown to be lower than that of standard techniques when the degree of the polynomial is large enough. Applications to the syndrome computation…
We provide estimates for weighted Fourier sums of integrable functions defined on the sphere when the weights originate from a multiplier operator acting on the space where the function belongs. That implies refined estimates for weighted…
The interpolation of couples of separable Hilbert spaces with a function parameter is studied. The main properties of the classic interpolation are proved. Some applications to the interpolation of isotropic H\"ormander spaces over a closed…
A method to isolate the poles of dimensionally regulated multi-loop integrals and to calculate the pole coefficients numerically is extended to be applicable to phase space integrals as well.