Alladi Ramakrishnan Hall

The Chowla problem and generalizations

M. Ram Murty

Queen's University, Canada

In 1969, Sarvadaman Chowla posed a simple question regarding non-vanishing of certain Dirichlet series attached to a periodic function. Four years later, Baker, Birch and Wirsing answered this question using Baker's theory of linear forms in logarithms subject to some restrictions on the periodic function. Their work left open the general question for an arbitrary periodic function. In this talk, we will give a complete characterisation of algebraic-valued periodic functions for which the associated L-series vanishes. This is a report on some recent joint work with Tapas Chatterjee and Siddhi Pathak.