Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: An Application of Hypergeometric Functions to Heat Kernels on
  Rectangular and Hexagonal Tori and a "Weltkonstante" -- Or -- How Ramanujan
  Split Temperatures   In this work we investigate the heat kernel of the Laplace--Beltrami operator
on a rectangular torus and the according temperature distribution. We compute
the minimum and the maximum of the temperature on rectangular tori of fixed
area by means of Gauss' hypergeometric function $_2F_1$ and the elliptic
modulus. In order to be able to do this, we employ a beautiful result of
Ramanujan, connecting hypergeometric functions, the elliptic modulus and theta
functions. Also, we investigate the temperature distribution of the heat kernel
on hexagonal tori and use Ramanujan's corresponding theory of signature 3 to
derive analogous results to the rectangular case. Lastly, we show connections
to the problem of finding the exact value of Landau's "Weltkonstante", a
universal constant arising in the theory of extremal holomorphic mappings; and
for a related, restricted extremal problem we show that the conjectured
solution is the second lemniscate constant.

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The categories of this paper are: hep-th
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The categories of this paper are: acc-phys
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The categories of this paper are: gr-qc
27
The categories of this paper are: comp-gas
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The categories of this paper are: bayes-an
31
The categories of this paper are: ao-sci
14
The categories of this paper are: math-ph
0
The categories of this paper are: hep-ph
32
The categories of this paper are: atom-ph
24
The categories of this paper are: dg-ga
29
The categories of this paper are: funct-an
12
The categories of this paper are: nucl-th
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The categories of this paper are: chao-dyn
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The categories of this paper are: adap-org
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The categories of this paper are: stat
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The categories of this paper are: eess