#### Alladi Ramakrishnan Hall

#### RAMANUJAN EXPANSIONS, SHIFTED CONVOLUTIONS & TWIN PRIMES

#### M. Ram Murty

##### Queen's University

*In 1914, Ramanujan introduced the notion of*

a "Fourier-type" expansion of an arithmetical function.

These expansions facilitate a smoother and systematic study

of convolutions sums. A special case of such a convolution

sum is related to the twin prime conjecture. We will

give a survey of this theory and also highlight some new

developments by discussing recent joint work

with Biswajyoti Saha and Giovanni Coppola.

Done