9 citations · 10 across the 5 of their papers we have counts for
6 papers
Tropical initial degeneration for systems of algebraic differential equations
Lara Bossinger, Sebastian Falkensteiner, Cristhian Garay-López +1
We study the notion of degeneration for affine schemes associated to systems of algebraic differential equations with coefficients in the fraction field of a multivariate formal po…
Siegel's theorem via the Lawrence-Venkatesh method
Marc Paul Noordman
In the recent paper arXiv:1807.02721, B. Lawrence and A. Venkatesh develop a method of proving finiteness theorems in arithmetic geometry by studying the geometry of families over…
Kummer surfaces for primality testing
Eduardo Ruíz Duarte, Marc Paul Noordman
We use the arithmetic of the Kummer surface associated to the Jacobian of a hyperelliptic curve to study the primality of integers of the form . We provide an algorithm…
The Fundamental Theorem of Tropical Partial Differential Algebraic Geometry
Sebastian Falkensteiner, Cristhian Garay-López, Mercedes Haiech +3
Tropical Differential Algebraic Geometry considers difficult or even intractable problems in Differential Equations and tries to extract information on their solutions from a restr…
Autonomous first order differential equations
Marc Paul Noordman, Marius van der Put, Jaap Top
The problem of algebraic dependence of solutions to (non-linear) first order autonomous equations over an algebraically closed field of characteristic zero is given a `complete' an…
The level of pairs of polynomials
Alberto F. Boix, Marc Paul Noordman, Jaap Top
Given a polynomial with coefficients in a field of prime characteristic , it is known that there exists a differential operator that raises to its th power. We firs…