Analytic Number Theory
Definition of Analytic Number Theory as it relates to Science, Mathematics
Analytic number theory is a branch of mathematics that employs methods from mathematical analysis to solve problems in number theory, the study of integers and their properties. It often involves the use of complex analysis, harmonic analysis, and differential equations to study the distribution of prime numbers, the Riemann zeta function, and other arithmetic functions. Analytic number theory has applications in cryptography, coding theory, and other areas of mathematics and computer science. At its core, analytic number theory is about understanding the structure and behavior of integers using the tools of calculus and higher mathematics.