Alladi Ramakrishnan Hall

Ramanujan expansions and twin primes

M. Ram Murty

Queen's University, Canada

In 1916, in a little known paper, Ramanujan introduced the idea
of a "Fourier series" for arithmetical functions. It is clear that
these ideas were in Ramanujan's mind before he left for England in 1914
since some of these notions are hinted at in his letters to Hardy written
earlier. In this talk, I will give a general outline of his ideas
and how they can be used to understand problems such as the twin
prime conjecture.