Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Abelian functions associated with a cyclic tetragonal curve of genus six   We develop the theory of Abelian functions defined using a tetragonal curve
of genus six, discussing in detail the cyclic curve $y^4 = x^5 + \lambda_4x^4 +
\lambda_3x^3 + \lambda_2x^2 + \lambda_1x + \lambda_0$. We construct Abelian
functions using the multivariate $\sigma$-function associated to the curve,
generalising the theory of the Weierstrass $\wp$-function. We demonstrate that
such functions can give a solution to the KP-equation, outlining how a general
class of solutions could be generated using a wider class of curves. We also
present the associated partial differential equations satisfied by the
functions, the solution of the Jacobi Inversion Problem, a power series
expansion for $\sigma(\bu)$ and a new addition formula.

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The categories of this paper are: ao-sci
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The categories of this paper are: nucl-ex
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The categories of this paper are: chem-ph
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The categories of this paper are: comp-gas
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The categories of this paper are: plasm-ph
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The categories of this paper are: econ
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The categories of this paper are: adap-org
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The categories of this paper are: chao-dyn
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The categories of this paper are: astro-ph
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The categories of this paper are: atom-ph
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The categories of this paper are: q-bio
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The categories of this paper are: hep-ex
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The categories of this paper are: q-fin
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The categories of this paper are: mtrl-th
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The categories of this paper are: dg-ga
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The categories of this paper are: acc-phys