Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Linear equations with unknowns from a multiplicative group in a function
  field   Let k be an algebraically closed field of characteristic 0, let K/k be a
transcendental extension of arbitrary transcendence degree and let G be a
multiplicative subgroup of (K^*)^n such that (k^*)^n is contained in G, and
G/(k^*)^n has finite rank r. We consider linear equations a1x1+...+anxn=1 (*)
with fixed non-zero coefficients a1,...,an from K, and with unknowns
(x1,...,xn) from the group G. Such a solution is called degenerate if there is
a subset of a1x1,...,anxn whose sum equals 0. Two solutions (x1,...,xn),
(y1,...,yn) are said to belong to the same (k^*)^n-coset if there are c1,...,cn
in k^* such that y1=c1*x1,...,yn=cn*xn. We show that the non-degenerate
solutions of (*) lie in at most 1+C(3,2)^r+C(4,2)^r+...+C(n+1,2)^r
(k^*)^n-cosets, where C(a,b) denotes the binomial coefficient a choose b.

30
The categories of this paper are: q-alg
33
The categories of this paper are: plasm-ph
13
The categories of this paper are: quant-ph
11
The categories of this paper are: hep-lat
32
The categories of this paper are: atom-ph
16
The categories of this paper are: stat
18
The categories of this paper are: econ
29
The categories of this paper are: funct-an
5
The categories of this paper are: gr-qc
36
The categories of this paper are: cmp-lg
7
The categories of this paper are: hep-th
15
The categories of this paper are: nucl-ex
0
The categories of this paper are: hep-ph
3
The categories of this paper are: physics
19
The categories of this paper are: eess
31
The categories of this paper are: ao-sci