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.