Related papers: Lambert series in analytic number theory

We provide a formal introduction into the classic theorems of general topology and its axiomatic foundations in set theory. Starting from ZFC, the exposition in this first part includes relation and order theory as well as a construction of…

This survey covers state-of-the-art Bayesian techniques for the estimation of mixtures. It complements the earlier Marin, Mengersen and Robert (2005) by studying new types of distributions, the multinomial, latent class and t distributions.…

This is a tutorial on some basic non-asymptotic methods and concepts in random matrix theory. The reader will learn several tools for the analysis of the extreme singular values of random matrices with independent rows or columns. Many of…

This is a introductory survey of some recent developments of "Galois ideas" in Arithmetic, Complex Analysis, Transcendental Number Theory and Quantum Field Theory, and of some of their interrelations.

In this paper we provide an overview of important research works on response-adaptive randomization completed in the past decades.

Time series, as one of the most fundamental representations of sequential data, has been extensively studied across diverse disciplines, including computer science, biology, geology, astronomy, and environmental sciences. The advent of…

This chapter aims at reviewing complex networks models and methods that were either developed for or applied to socioeconomic issues, and pertinent to the theme of New Economic Geography. After an introduction to the foundations of the…

This paper presents a short introduction to local fractional complex analysis. The generalized local fractional complex integral formulas, Yang-Taylor series and local fractional Laurent's series of complex functions in complex fractal…

This article discusses recent developments in the literature of quantile time series models in the cases of stationary and nonstationary underline stochastic processes.

We prove theorems of interest about the recently given $\Lambda^{r}$-strong convergence. We extend the results of F. M\'oricz [On $\Lambda$-strong convergence of numerical sequences and Fourier series, Acta Math.~Hungar., 54 (1989),…

The purpose of this article is to present, in a simple way, an analytic approach to special numbers and polynomials. The approach is based on the derivative polynomials. The paper is, to some extent, a review article, although it contains…

Time series analysis is relevant in various disciplines such as physics, biology, chemistry, and finance. In this paper, we present a novel neural network architecture that integrates elements from ResNet structures, while introducing the…

A partly autobiographical survey of the development of enumerative and algebraic combinatorics in the 1960's and 1970's.

BERT, as one of the pretrianed language models, attracts the most attention in recent years for creating new benchmarks across GLUE tasks via fine-tuning. One pressing issue is to open up the blackbox and explain the decision makings of…

I discuss comments and claims made in Stehlik and Hermann (2015) about skewed Lambert W x F random variables and the IGMM algorithm. I clarify misunderstandings about the definition and use of Lambert W x F distributions and show that most…

A collection of articles on the statistical modelling and inference of social networks is analysed in a network fashion. The references of these articles are used to construct a citation network data set, which is almost a directed acyclic…

We give explicit expressions (or at least an algorithm of obtaining such expressions) of the coefficients of the Laurent series expansions of the Euler-Zagier multiple zeta-functions at any integer points. The main tools are the…

While there are numerous linear algebra teaching tools, they tend to be focused on the basics, and not handle the more advanced aspects. This project aims to fill that gap, focusing specifically on methods like Strassen's fast matrix…

This is a survey article on some recent developments in the arithmetic theory of linear algebraic groups over higher-dimensional fields, written for the Notices of the AMS.

This is a textbook about elementary number theory, with emphasis on classical topics around the Euklidean Algorithm.