Related papers: Special functions, transcendentals and their numer…

In this paper, algorithms are developed for computing the Stirling transform and the inverse Stirling transform; specifically, we investigate a class of sequences satisfying a two-term recurrence. We derive a general identity which…

We consider here a particular quadratic equation linking two elements of a C-Algebra. By analysing powers of the unknowns, it appears a double sequence of polynomials related to classical Bernoulli polynomials. We get the generating…

In the first part of this expository paper, we present and discuss the interplay of Dirichlet polynomials in some classical problems of number theory, notably the Lindel\"of Hypothesis. We review some typical properties of their means and…

Discrete analogs of the index transforms, involving Bessel and Lommel functions are introduced and investigated. The corresponding inversion theorems for suitable classes of functions and sequences are established.

We discuss and prove a number of results for calculating characteristic cycles, or graded, enriched characteristic cycles. We concentrate particularly on results related to hypersurfaces.

The present article is devoted to the description of further investigations of the author of this article. These investigations (in terms of various representations of real numbers) include the generalized Salem functions and…

We present recent phenomenological studies, tailored on kinematic configurations typical of current and forthcoming analyses at the LHC, for two novel probe channels of the BFKL resummation of energy logarithms. Particular attention is…

In this paper, we study some properties of multivariate gamma function and zonal polynomials.

The computation of Feynman integrals in massive higher order perturbative calculations in renormalizable Quantum Field Theories requires extensions of multiply nested harmonic sums, which can be generated as real representations by Mellin…

Expanding upon recent work, a new class of $A$-functions is introduced that can be viewed as an appropriate generalization of the class of regular $A$-functions, the class of structured $A$-functions, and the class of perfect $A$-functions.…

Several estimates for singular integrals, maximal functions and the spherical summation operator are given in the spaces $L^p_{\text{rad}}L^2_{\text{ang}}(\mathbb{R}^n)$, $n\geq 2$.

In these lectures I discuss Feynman graphs and the associated Feynman integrals. Of particular interest are the classes functions, which appear in the evaluation of Feynman integrals. The most prominent class of functions is given by…

This article reviews the arguments why extra dimensions provide a unique opportunity for progress on the cosmological constant problem, and updates the status of -- and the objections to (with replies) -- the specific proposal using…

This thesis is intended to provide an account of the theory and applications of Operational Methods that allow the "translation" of the theory of special functions and polynomials into a "different" mathematical language. The language we…

In this note, we establish some new results on some special types of function algebras and also give new proofs to some existing ones

Attempting to create a general framework for studying new results on transcendental numbers, this paper begins with a survey on transcendental numbers and transcendence, it then presents several properties of the transcendental numbers $e$…

This is a copy of the article published in Math Res. Letters 5, (1998) 497-516.

We introduce the continued logarithm representation of real numbers and prove results on the occurrence and frequency of digits with respect to this representation

We give a number of theoretical and practical methods related to the computation of L-functions, both in the local case (counting points on varieties over finite fields, involving in particular a detailed study of Gauss and Jacobi sums),…

In the paper I study properties of random polynomials with respect to a general system of functions. Some lower bounds for the mathematical expectation of the uniform and recently introduced integral-uniform norms of random polynomials are…