NON-ARCHIMEDEAN YOMDIN–GROMOV PARAMETRIZATIONS AND POINTS OF BOUNDED HEIGHT

Autor: RAF CLUCKERS, GEORGES COMTE, FRANÇOIS LOESER

Publikováno v: Forum of Mathematics, Pi, Vol 3 (2015)

We prove an analog of the Yomdin–Gromov lemma for $p$-adic definable sets and more broadly in a non-Archimedean definable context. This analog keeps track of piecewise approximation by Taylor polynomials, a nontrivial aspect in the totally disconne

Externí odkaz: https://doaj.org/article/1f35315cded34ee0908436aa10db1c83

Points of bounded height on oscillatory sets

Autor: Georges Comte, Chris Miller

Publikováno v: The Quarterly Journal of Mathematics. 68:1261-1287

— We show that transcendental curves in R (not necessarily compact) have few rational points of bounded height provided that the curves are well behaved with respect to algebraic sets and can be parametrized by functions belonging to a specified al

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::1749df462247f1d7989efde2bcdfff2a
https://doi.org/10.1093/qmath/hax021

M subdwarf research. I. Identification, modified classification system, and sample construction

Autor: Yu Bai, Li Qin, Xiao Kong, John E. Gizis, Shuo Zhang, A-Li Luo, Zhenping Yi, Yin-Bi Li, Rui Wang, Georges Comte

Publikováno v: Astrophysical Journal Supplement
Astrophysical Journal Supplement, American Astronomical Society, 2019, 240 (2), pp.31. ⟨10.3847/1538-4365/aafb32⟩
The Astrophysical Journal Supplement
The Astrophysical Journal Supplement, 2019, 240 (2), pp.31. ⟨10.3847/1538-4365/aafb32⟩

We propose a revision of the system developed by L'epine et al. (2007) for spectroscopic M subdwarf classification. Based on an analysis of subdwarf spectra and templates from Savcheva et al. (2014), we show thatthe CaH1 feature originally proposed b

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::963fed50901ef934ecb1106d5b89a05e

Zeroes and rational points of analytic functions

Autor: Georges Comte, Yosef Yomdin

For an analytic function $f(z)=\sum_{k=0}^\infty a_kz^k$ on a neighbourhood of a closed disc $D\subset {\bf C}$, we give assumptions, in terms of the Taylor coefficients $a_k$ of $f$, under which the number of intersection points of the graph $\Gamma

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::64b687c4fbc32687b43dbc7e46cdd247
http://arxiv.org/abs/1608.02455

Lipschitz Continuity Properties for p−Adic Semi-Algebraic and Subanalytic Functions

Autor: Raf Cluckers, François Loeser, Georges Comte

Publikováno v: Geometric and Functional Analysis. 20:68-87

We prove that a (globally) subanalytic function f : X ⊂ Q n → Qp which is locally Lipschitz continuous with some constant C is piecewise (globally on each piece) Lipschitz continuous with possibly some other constant, where the pieces can be take

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_________::30048615f183ffc9b45ed9171d5e6223
https://doi.org/10.1007/s00039-010-0060-0