Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A p-adic analogue of Siegel's Theorem on sums of squares   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. The p-adic Kochen operator provides a p-adic
analogue of squaring, and a certain localisation of the ring generated by this
operator consists of precisely the totally p-integral elements of K. We use
this to formulate and prove a p-adic analogue of Siegel's theorem, by
introducing the p-Pythagoras number of a general field, and showing that this
number is uniformly bounded across number fields. We also generally study
fields with finite p-Pythagoras number and show that the growth of the
p-Pythagoras number in finite extensions is bounded.

7
The categories of this paper are: hep-th
29
The categories of this paper are: funct-an
36
The categories of this paper are: cmp-lg
18
The categories of this paper are: econ
12
The categories of this paper are: nucl-th
3
The categories of this paper are: physics
6
The categories of this paper are: astro-ph
28
The categories of this paper are: alg-geom
17
The categories of this paper are: q-fin
27
The categories of this paper are: comp-gas
30
The categories of this paper are: q-alg
33
The categories of this paper are: plasm-ph
10
The categories of this paper are: q-bio
34
The categories of this paper are: chem-ph
23
The categories of this paper are: solv-int
14
The categories of this paper are: math-ph