Singular Gauss sums, Polya-Vinogradov inequality for $GL(2)$ and growth of primitive elements

Satadal Ganguly, C. S. Rajan

We establish an analogue of the classical Polya-Vinogradov inequality for $GL(2, \F_p)$, where $p$ is a prime. In the process, we compute the `singular' Gauss sums for $GL(2, \F_p)…