3 papers
math.NT2019
A p-adic analogue of Siegel's Theorem on sums of squares
Sylvy Anscombe, Philip Dittmann, Arno Fehm
Siegel proved that every totally positive element of a number field K is the sum of four squares, so in particular the Pythagoras number is uniformly bounded across number fields.…
math.AC2019
Approximation theorems for spaces of localities
Sylvy Anscombe, Philip Dittmann, Arno Fehm
The classical Artin--Whaples approximation theorem allows to simultaneously approximate finitely many different elements of a field with respect to finitely many pairwise inequival…
math.LO2017
Existentially generated subfields of large fields
Sylvy Anscombe
We study subfields of large fields which are generated by infinite existentially definable subsets. We say that such subfields are existentially generated. Let be a large field…