4 papers
The dimension growth conjecture, polynomial in the degree and without logarithmic factors
Wouter Castryck, Raf Cluckers, Philip Dittmann +1
We address Heath-Brown's and Serre's dimension growth conjecture (proved by Salberger), when the degree grows. Recall that Salberger's dimension growth results give bounds of t…
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.…
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…
Defining Subrings in Finitely Generated Fields of All Characteristics
Philip Dittmann
We give a construction of a large first-order definable family of subrings of finitely generated fields of any characteristic. We deduce that for any such there exists a fi…