Recent Progress in Number Theory: Analytic and Computational Perspectives

Abstract

Number theory has experienced significant development in recent decades through the integration of classical analytic techniques and modern computational methods. This paper presents an overview of recent progress in number theory with particular emphasis on analytic and computational perspectives. Analytic number theory provides powerful tools for studying the distribution of prime numbers, arithmetic functions, and zeta and L-functions, while computational number theory enables large-scale numerical experimentation, algorithmic verification of conjectures, and practical applications in cryptography and computer science.