Divergent Series

This project is for a student who finds the following result shocking but intriguing:

1 + 2 + 3 + . . . = -1/12

This looks wrong in so many ways what with the sum of positive terms being negative and an infinite sum being finite. The aim of the project is to understand why this and other similar results are not completely crazy and, in fact, hint at a deeper role for divergent series in various areas of mathematics and its applications. The background for this project is covered in MATH2405 (Real and Complex Analysis).

Literature: G.H. Hardy, Divergent Series. Clarendon Press, Oxford. 1949 (a free ebook version is on the web)

Supervisor: Prof David McMullan