  We prove sharp $L^{12}$ estimates for exponential sums associated with
nondegenerate curves in ${\mathbb R}^4$. We place Bourgain's progress on the
Lindel"of hypothesis in a larger framework that contains a continuum of
estimates of different flavor. We enlarge the spectrum of methods by combining
decoupling with quadratic Weyl sum estimates, to address new cases of interest.
All results are proved in the general framework of real analytic curves.
