#### 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.

Done