Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Zeta functions and Bernstein-Sato polynomials for ideals in dimension
  two   For a nonzero ideal I of C[x_1,...,x_n], with 0 in supp I, a generalization
of a conjecture of Igusa - Denef - Loeser predicts that every pole of its
topological zeta function is a root of its Bernstein-Sato polynomial. However,
typically only a few roots are obtained this way. Following ideas of Veys, we
study the following question. Is it possible to find a collection G of
polynomials g in C[x_1,...,x_n], such that, for all g in G, every pole of the
topological zeta function associated to I and the volume form gdx on the affine
n-space, is a root of the Bernstein-Sato polynomial of I, and such that all
roots are realized in this way. We obtain a negative answer to this question,
providing counterexamples for monomial and principal ideals in dimension two,
and give a partial positive result as well.

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The categories of this paper are: hep-ph
13
The categories of this paper are: quant-ph
4
The categories of this paper are: cond-mat
23
The categories of this paper are: solv-int
15
The categories of this paper are: nucl-ex
17
The categories of this paper are: q-fin
9
The categories of this paper are: nlin
1
The categories of this paper are: cs
34
The categories of this paper are: chem-ph
36
The categories of this paper are: cmp-lg
25
The categories of this paper are: patt-sol
30
The categories of this paper are: q-alg
16
The categories of this paper are: stat
19
The categories of this paper are: eess
32
The categories of this paper are: atom-ph
12
The categories of this paper are: nucl-th