Khovanskii's format-bound conjecture for Noetherian functions

Let P{\mathcal P} be the domain of a Noetherian chain and let P1,,Pn:PCP_1,\ldots,P_n:{\mathcal P}\to\mathbb C be Noetherian functions of format F{\mathscr F}. Khovanskii's format-bound conjecture. The number of isolated points in

{zP:P1(z)==Pn(z)=0}\{ {\mathbf z}\in{\mathcal P}:P_1({\mathbf z})=\cdots=P_n({\mathbf z})=0\}

is bounded by some explicit function of F{\mathscr F}. This is a stronger global form of the local conjecture and must account for coefficient sizes and function magnitudes, which are included in the format.

Sources & referencesView supporting material

Primary source

Gal Binyamini, “Log-Noetherian functions”, arXiv:2405.16963 (2024).

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