Alladi Ramakrishnan Hall

Automorphy and the Sato-Tate Conjecture

M. Ram Murty

Queen's University, Canada

Beginning with a discussion of the 1916 paper by
Ramanujan on the celebrated tau function, we present the Sato-Tate conjecture related to it. We then proceed to show how a special
case of the Langlands functoriality conjecture would lead to automorphy
of the symmetric power L-functions attached to tau. This work has
several applications and I will discuss these results obtained jointly
with V. Kumar Murty and Sanoli Gun.