Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Renormalization : A number theoretical model   We analyse the Dirichlet convolution ring of arithmetic number theoretic
functions. It turns out to fail to be a Hopf algebra on the diagonal, due to
the lack of complete multiplicativity of the product and coproduct. A related
Hopf algebra can be established, which however overcounts the diagonal. We
argue that the mechanism of renormalization in quantum field theory is modelled
after the same principle. Singularities hence arise as a (now continuously
indexed) overcounting on the diagonals. Renormalization is given by the map
from the auxiliary Hopf algebra to the weaker multiplicative structure, called
Hopf gebra, rescaling the diagonals.

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The categories of this paper are: ao-sci
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The categories of this paper are: quant-ph
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The categories of this paper are: cmp-lg
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The categories of this paper are: gr-qc
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The categories of this paper are: chem-ph
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The categories of this paper are: nlin
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The categories of this paper are: plasm-ph
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The categories of this paper are: supr-con
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The categories of this paper are: dg-ga
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The categories of this paper are: econ
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The categories of this paper are: chao-dyn
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The categories of this paper are: alg-geom
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The categories of this paper are: patt-sol
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The categories of this paper are: physics
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The categories of this paper are: acc-phys
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The categories of this paper are: q-fin