Alladi Ramakrishnan Hall

Circle method and the subconvexity problem

Ritabrata Munshi

ISI Kolkata

Almost a hundred years back Weyl and Hardy-Littlewood established the first subconvexity bound for the Riemann zeta function $\zeta(1/2+it)\ll t^{1/6+\varepsilon}$ (say $t>2$). The exponent has been reduced to 13/84=0.1548 in a recent paper of Bourgain - a culmination of decades of hard work of a number of leading mathematicians in the field. In 1980's Good established the analog of the Weyl bound in the case of the degree two L-functions. This still remains unbeaten. The main focus of the talk will be this particular aspect of subconvexity in the case of L-functions of degrees one, two and three.