Related papers: Laurent type expansion of multiple polylogarithms …
We present an algorithm for efficient computation of the constant term of a power of a multivariate Laurent polynomial. The algorithm is based on univariate interpolation, does not require the storage of intermediate data and can be easily…
In this paper, we begin by reviewing the calculus induced by the framework of [10]. In there, we extended Polylogarithm functions over a subalgebra of noncommutative rational power series, recognizable by finite state (multiplicity)…
The Barnes multiple zeta function is useful to study in the number theory and Knot thoey and Mathematical Physics. In this paper we consider q-extension of Barnes type multiple zeta function and we also construct the q-extension of Euler…
In this paper we investigate a class of integrals that were encountered in the course of a work on statistical plasma physics, in the so-called Sommerfeld temperature-expansion of the electronic entropy. We show that such integrals,…
Based on Guillemin's work on gauged Lagrangian distributions, we will introduce the notion of a poly-$\log$-homogeneous distribution as an approach to $\zeta$-functions for a class of Fourier Integral Operators which includes cases of…
Ehrhart's famous theorem states that the number of integral points in a rational polytope is a quasi-polynomial in the integral dilation factor. We study the case of rational dilation factors and it turns out that the number of integral…
An ordering for Laurent polynomials in the algebraic torus $(\mathbb C^*)^D$, inspired by the Cantero-Moral-Vel\'azquez approach to orthogonal Laurent polynomials in the unit circle, leads to the construction of a moment matrix for a given…
Some results of microlocal continuity for pseudodifferential operators whose non regular symbols belong to weighted Fourier Lebesgue spaces are given. Inhomogeneous local and microlocal propagation of singularities of Fourier Lebesgue type…
In this paper, we explore the inflectionary behavior of linear series on superelliptic curves $X$ over fields of arbitrary characteristic. Here we give a precise description of the inflection of linear series over the ramification locus of…
Maximon has recently given an excellent summary of the properties of the Euler dilogarithm function and the frequently used generalizations of the dilogarithm, the most important among them being the polylogarithm function $Li_(z)$. The…
We define a new generalization of Catalan numbers to multinomial coefficients. With arithmetic methods, we study their integrality and the integrality of their Lucasnomial generalization. We give a complete characterization of regular Lucas…
We study the correlation functions of logarithmic conformal field theories. First, assuming conformal invariance, we explicitly calculate two-- and three-- point functions. This calculation is done for the general case of more than one…
We derive formulae for the calculation of Taylor coefficients of solutions to systems of Volterra integral equations, both linear and nonlinear, either without singularities or with singularities of Abel type and logarithmic type. We also…
We study Toeplitz-type operators with respect to specific wavelets whose Fourier transforms are related to Laguerre polynomials. On the one hand, this choice of wavelets underlines the fact that these operators acting on wavelet subspaces…
The function $ \tan(\pi x / 2) / (\pi x / 2) $ is expanded into a Laurent series of $ 1 - x^2 $, where the coefficients are given explicitly as combinations of zeta function of even integers. This is used to achieve a sequence of upper and…
Linearized polynomials appear in many different contexts, such as rank metric codes, cryptography and linear sets, and the main issue regards the characterization of the number of roots from their coefficients. Results of this type have…
Local Fourier analysis is a strong and well-established tool for analyzing the convergence of numerical methods for partial differential equations. The key idea of local Fourier analysis is to represent the occurring functions in terms of a…
A local lattice point counting formula, and more generally a local Euler-Maclaurin formula follow by comparing two natural families of meromorphic functions on the dual of a rational vector space $V$, namely the family of exponential sums…
A discussion of how to calculate asymptotic expansions for polyhomogeneous spacetimes using the Newman-Penrose formalism is made. The existence of logarithmic Newman-Penrose constants for a general polyhomogeneous spacetime (i.e. a…
We study the local solvability of a class of operators with multiple characteristics. The class considered here complements and extends the one studied in [9], in that in this paper we consider some cases of operators with complex…