Preface

Number theory and its applications are well known for their proven properties and excellent applicability in interdisciplinary fields of science.

This book contains a collection of selected and refereed papers on the most recent developments in number theory and its applications.

There are so many topics related to number theory that it is hard to list them all, but potential topics include, but are not limited to, the following:


The editor of this book sought to cover various aspects of the number theory and its applications in the current project by introducing a variety of welcoming themes from the international audience of mathematicians and researchers. The editor has organized chapters as a result of research by a group of leading researchers in the number theory and related fields. The goal of this book is to provide an overview of the current research in the field of number theory and its applications.

The main subject areas are divided into number theory and its applications.

These include "A new integer-to-integer transform", "Digit sums and infinite products", "The Borel-Cantelli lemmas, and their relationship to limit superior and limit inferior of sets", "Prime numbers distribution line", "Moments of catalan triangle numbers", "Modular sumset labelling of graphs", "Determination of the properties of (*p, q*)-sigmoid polynomials and the structure of their roots", "I–convergence of arithmetical functions", "Identification of eigen-frequencies and mode-shapes of beams with continuous distribution of mass and elasticity and for various conditions at supports", "Some identities involving 2-variable modified degenerate Hermite polynomials arising from differential equations and distribution of their zeros", and "Elliptic curve over a local finite ring *Rn*".

We hope that this book will be timely and fill a gap in the literature on the number theory and related fields. We also hope that it will promote further research and development in this important field.

Thanks to the authors for their creative contributions and the reviewers for their prompt and careful reviews.

> **Cheon Seoung Ryoo** Professor, Hannam University, South Korea

> > Section 1

Number Theory
