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Normalizing Asymptotic Differential Equations
Matthias Aschenbrenner, Lou van den Dries, Joris van der Hoeven
We define the universal exponential extension of an algebraically closed differential field and investigate its properties in the presence of a nice valuation and in connection wit…
Constructing -free Hardy fields
Matthias Aschenbrenner, Lou van den Dries, Joris van der Hoeven
We show that every Hardy field extends to an -free Hardy field. This result relates to classical oscillation criteria for second-order homogeneous linear differential equations…
The reciprocal complement of a polynomial ring in several variables over a field
Neil Epstein, Lorenzo Guerrieri, K. Alan Loper
The *reciprocal complement* of an integral domain is the subring of its fraction field generated by the reciprocals of its nonzero elements. Many properties of ar…