Analytic number theory deals with the application of analysis, both real and complex, to the study of numbers. It includes primes, transcendental numbers, diophantine equations and other questions. The study of the Riemann zeta-function $\zeta(s)$ is intimately connected with that of primes. \par In this note, edited specially for this volume by K. Srinivas, some problems from a handwritten manuscript of Ramachandra are listed.