Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Complexity results for CR mappings between spheres   Using elementary number theory, we prove several results about the complexity
of CR mappings between spheres. It is known that CR mappings between spheres,
invariant under finite groups, lead to sharp bounds for degree estimates on
real polynomials constant on a hyperplane. We show here that there are
infinitely many degrees for which the uniqueness of sharp examples fails. The
proof uses a Pell equation and complicated explicit computations. We also show
that the so-called gap phenomenon for proper mappings between balls does not
occur beyond a certain target dimension. This proof uses the solution of the
postage stamp problem.

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The categories of this paper are: atom-ph
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The categories of this paper are: plasm-ph
10
The categories of this paper are: q-bio
0
The categories of this paper are: hep-ph
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The categories of this paper are: quant-ph
5
The categories of this paper are: gr-qc
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The categories of this paper are: hep-lat
4
The categories of this paper are: cond-mat
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The categories of this paper are: supr-con
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The categories of this paper are: stat
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The categories of this paper are: funct-an
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The categories of this paper are: cmp-lg
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The categories of this paper are: solv-int
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The categories of this paper are: q-alg
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The categories of this paper are: ao-sci
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The categories of this paper are: eess