Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A Complete Hypergeometric Point Count Formula for Dwork Hypersurfaces   We extend our previous work on hypergeometric point count formulas by proving
that we can express the number of points on families of Dwork hypersurfaces
$$X_{\lambda}^d: \hspace{.1in} x_1^d+x_2^d+\ldots+x_d^d=d\lambda x_1x_2\cdots
x_d$$ over finite fields of order $q\equiv 1\pmod d$ in terms of Greene's
finite field hypergeometric functions. We prove that when $d$ is odd, the
number of points can be expressed as a sum of hypergeometric functions plus
$(q^{d-1}-1)/(q-1)$ and conjecture that this is also true when $d$ is even. The
proof rests on a result that equates certain Gauss sum expressions with finite
field hypergeometric functions. Furthermore, we discuss the types of
hypergeometric terms that appear in the point count formula and give an
explicit formula for Dwork threefolds.

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The categories of this paper are: acc-phys
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The categories of this paper are: q-bio
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The categories of this paper are: q-alg
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The categories of this paper are: hep-lat
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The categories of this paper are: nucl-ex
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The categories of this paper are: chao-dyn
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The categories of this paper are: bayes-an
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The categories of this paper are: supr-con
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The categories of this paper are: quant-ph
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The categories of this paper are: cs
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The categories of this paper are: astro-ph
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The categories of this paper are: patt-sol
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The categories of this paper are: funct-an
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The categories of this paper are: nucl-th
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The categories of this paper are: econ
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The categories of this paper are: alg-geom