On Conservative Matrix Fields: Continuous Asymptotics and Arithmetic

We present the Conservative Matrix Field (CMF) as a tool for the analysis and computation of D-finite functions.

We use conservative matrix fields to establish asymptotic properties of families of linear forms in periods, including (but not limited to) multivariate Mellin integrals, via a discrete Levinson-type framework due to Benzaid and Lutz.

Finally, we present an experimental analysis of the families of linear forms generated by these objects and formalize the resulting observations as conjectures on their continuous asymptotic and arithmetic properties.