Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Irrational behavior of algebraic discrete valuations   We study algebraic discrete valuations dominating normal local domains of
dimension two. We construct a family of examples to show that the
Hilbert-Samuel function of the associated graded ring of the valuation can fail
to be asymptotically of the form: quasi-polynomial plus a bounded function. We
also show that the associated multiplicity can be irrational, or even
transcendental.

23
The categories of this paper are: solv-int
13
The categories of this paper are: quant-ph
25
The categories of this paper are: patt-sol
24
The categories of this paper are: dg-ga
33
The categories of this paper are: plasm-ph
32
The categories of this paper are: atom-ph
37
The categories of this paper are: supr-con
29
The categories of this paper are: funct-an
16
The categories of this paper are: stat
3
The categories of this paper are: physics
8
The categories of this paper are: hep-ex
14
The categories of this paper are: math-ph
34
The categories of this paper are: chem-ph
1
The categories of this paper are: cs
26
The categories of this paper are: bayes-an
18
The categories of this paper are: econ