Publications > Preprint server > Preprint Number 2641
Preprint Number 2641
2641. Gal Binyamini Log-Noetherian functions E-mail: Submission date: 27 May 2024 Abstract:
We introduce the class of Log-Noetherian (LN) functions. These are
holomorphic solutions to algebraic differential equations (in several
variables) with logarithmic singularities. We prove an upper bound on the
number of solutions for systems of LN equations, resolving in particular
Khovanskii's conjecture for Noetherian functions. Consequently, we show that
the structure ℝ_{LN} generated by LN-functions, as well as its
expansion ℝ_{LN,exp}, are effectively o-minimal: definable
sets in these structures admit effective bounds on their complexity in terms of
the complexity of the defining formulas. Mathematics Subject Classification: 03C64, 58A17, 14D07, 14Q201 Keywords and phrases: |
Last updated: June 10 2024 21:20 | Please send your corrections to: |