Related papers: Lambert series in analytic number theory

The Lambert W(x) function and its possible applications in physics are presented. The actual numerical implementation in C++ consists of Halley's and Fritsch's iterations with initial approximations based on branch-point expansion,…

This is a survey of old and new problems and results in additive number theory.

This is an anthology of series involving rational, factorial, and power functions expressed in terms of special functions. New finite expansions involving quotient functions expressed in terms of the Hurwitz-Lerch zeta function are given.…

This is an introductory article to the theory of multiple gaps.

An interplay between the Lambert series and Euler's Pentagonal Number Theorem gives an Euler-type recurrence relation for any given arithmetical function. As consequences of this, we present Euler-type recurrence relations for some…

In the following article we consider approximate Bayesian computation (ABC) for certain classes of time series models. In particular, we focus upon scenarios where the likelihoods of the observations and parameter are intractable, by which…

The review is a brief description of the state of problems in percolation theory and their numerous applications, which are analyzed on base of interesting papers published in the last 15-20 years. At the submitted papers are studied both…

This article considers to model large-dimensional matrix time series by introducing a regression term to the matrix factor model. This is an extension of classic matrix factor model to incorporate the information of known factors or useful…

In this book, there are five chapters: Systems of Linear Equations, Vector Spaces, Homogeneous Systems, Characteristic Equation of Matrix, and Matrix Dot Product. It has also exercises at the end of each chapter above to let students…

This survey on approximations of perturbed operator functions addresses recent advances and some of the successful methods.

This paper is now part of the new paper "Series with Hermite polynomials and applications" arXiv:1710.00687.

This article surveys recent progress in the Bradley-Terry (BT) model and its extensions. We focus on the statistical and computational aspects, with emphasis on the regime in which both the number of objects and the volume of comparisons…

Notions of quasi-classical Lie-super algebra as well as Lie-super triple systems have been given and studied with some examples. Its application to Yang-Baxter equation has also been given.

Commentary on Emil Artin's "Uber eine neue Art von L-Reihen" (1924), including a modernized and expanded translation.

Part I. Some Facts From p-Adic Analysis. Part II. Tables of Integrals.

The second author has recently introduced a new class of L-series in the arithmetic theory of function fields over finite fields. We show that the value at one of these L-series encode arithmetic informations of certain Drinfeld modules…

A mixture of an historical article, and of a survey of recent developments, containing also a couple of new results.

The Slater-type orbital basis with non-integer principal quantum numbers is a physically and mathematically motivated choice for molecular electronic structure calculations in both non-relativistic and relativistic theory. The…

Time series data plays a critical role across diverse domains such as healthcare, energy, and finance, where tasks like classification, anomaly detection, and forecasting are essential for informed decision-making. Recently, large language…

We survey the classical results of the Dirichlet Approximation Theorem.