Analytic number Theory
We shall prove the classical theorems on the distribution of prime numbers in strong analytic form. You will meet the basic objects and techniques of analytic number theory such as Dirichlet L-functions and the Mellin transform. You will develop a deeper understanding of numbers, complex analysis, and the Riemann Hypothesis.
The main goal of the course is to introduce students to the main topics and methods of Analytic Number Theory.
By the end of the course, students are enabled to do independent study and research in fields touching on the topics of the course, and how to use these methods to solve specific problems. In addition, they develop some special expertise in the topics covered, which they can use efficiently in other mathematical fields, and in applications, as well. They also learn how the topic of the course is interconnected to various other fields in mathematics, and in science, in general.
- regular homework, and presentation or final