# Hilbert's Nullstellensatz Is in the Polynomial Hierarchy

@article{Koiran1996HilbertsNI,
title={Hilbert's Nullstellensatz Is in the Polynomial Hierarchy},
author={Pascal Koiran},
journal={J. Complex.},
year={1996},
volume={12},
pages={273-286}
}
• P. Koiran
• Published 30 July 1996
• Computer Science, Mathematics
• J. Complex.
We show that if the Generalized Riemann Hypothesis is true, the problem of deciding whether a system of polynomial equations in several complex variables has a solution is in the second level of the polynomial hierarchy. In fact, this problem is in AM, the Arthur-Merlin'''' class (recall that $\np \subseteq \am \subseteq \rp^{\tiny \np} \subseteq \Pi_2$). The best previous bound was PSPACE. An earlier version of this paper was distributed as NeuroCOLT Technical Report~96-44. The present paper… Expand
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