Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A view on elliptic integrals from primitive forms (Period integrals of
  type $\mathrm{A_2, B_2}$ and $\mathrm{G_2}$   Elliptic integrals, since Euler's finding of addition theorem 1751, has been
studied extensively from various view points. Present paper gives a view point
from primitive integrals of types $\mathrm{A_2}, \mathrm{B_2}$ and
$\mathrm{G_2}$ for the three families of elliptic curves of Weierstrass,
Jacobi-Legendre and Hesse, respectively. We solve Jacobi inversion problem for
the period maps in the sense explained in the introduction (see [Siegel]
Chap.1,13) by introducing certain generalized Eisenstein series of types
$\mathrm{A_2}, \mathrm{B_2}$ and $\mathrm{\mathrm{G_2}}$, which generate the
ring of invariant functions on the period domain for the congruence subgroups
$\Gamma_1(N)$ ($N=1,2$ and $3$). In particular, Eisenstein series of type
$\mathrm{B_2}$ includes the case of weight two, and Eisenstein series of type
$\mathrm{G_2}$ includes the cases of weight one and two, which seem to be of
new feature. The goal of the paper is a partial answer to the discriminant
conjecture, which claims an existence of certain cusp form of weight 1 with
character of topological origin, giving a power root of the discriminant form
(Aspects Math., E36,p.\ 265-320.\ 2004). See \S12 Concluding Remarks for more
about back grounds of the present paper.

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The categories of this paper are: quant-ph
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The categories of this paper are: math-ph
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The categories of this paper are: nlin
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The categories of this paper are: chao-dyn
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The categories of this paper are: cmp-lg
34
The categories of this paper are: chem-ph
5
The categories of this paper are: gr-qc
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The categories of this paper are: alg-geom
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The categories of this paper are: stat
0
The categories of this paper are: hep-ph
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The categories of this paper are: plasm-ph
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The categories of this paper are: patt-sol
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The categories of this paper are: acc-phys
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The categories of this paper are: cs
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The categories of this paper are: mtrl-th
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The categories of this paper are: atom-ph