Analytical Number Theory

Analytical Number Theory is a branch of mathematics that uses tools from analysis—like calculus and infinite series—to study properties of numbers, especially prime numbers. It seeks to understand the distribution and behavior of these numbers by translating arithmetic questions into questions about functions, limits, and patterns. This approach has led to deep results, such as the Prime Number Theorem, which describes how primes are spread out among all numbers. Essentially, it combines methods from different areas of mathematics to unravel the mysteries of integers and their fundamental properties.