Analytic number theory is a branch of mathematics that deals with the relationship between prime numbers and other number-theoretic functions. It involves the use of techniques from analysis, such as complex analysis, to study properties of integers and prime numbers. Some key topics in analytic number theory include the distribution of prime numbers, the Riemann zeta function, and the study of arithmetic functions. Researchers in this field often work on problems related to prime number theory, the Riemann hypothesis, and other unsolved questions in number theory.