No.178 Seminar ： How do prime numbers decompose?
- Assistant Professor Masao OI (Hakubi 10th batch,Graduate School of Science)
- 2020/01/28 4:30pm
- Conference Room 1&2,The first basement floor, Research Administration Building(Hakubi Center building)
- English
- Closed (only staff of Kyoto University)
Summary
Any prime number cannot be decomposed into a product of smaller integers by its definition.
However, this is a story in the world of usual integers.
As every quadratic equation has a solution in the world of complex numbers, in modern mathematics, we often consider a framework which is larger than usual system of numbers and investigate phenomena happening there.
In such a framework, sometimes prime numbers can be decomposed into a product of smaller “integers” (in an extended sense).
In fact, studying such a decomposition of prime numbers in an extended world leads us to so-called the Langlands conjecture, which plays a very important role in modern number theory.
In this seminar, by using several example of phenomena of prime numbers observed by Fermat and Ramanujan, I would like to explain what the Langlands conjecture is and also an approach to this conjecture.