# Tschirnhaus transformations after Hilbert

@article{Wolfson2020TschirnhausTA, title={Tschirnhaus transformations after Hilbert}, author={Jesse Wolfson}, journal={arXiv: Algebraic Geometry}, year={2020} }

Let RD(n) denote the minimum d for which there exists a formula for the roots of the general degree n polynomial using only algebraic functions of d or fewer variables. In 1927, Hilbert sketched how the 27 lines on a cubic surface could be used to construct a 4-variable formula for the general degree 9 polynomial (implying $RD(9)\le 4$). In this paper, we turn Hilbert's sketch into a general method. We show this method produces best-to-date upper bounds on RD(n) for all n, improving earlier… Expand

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