Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Universal elliptic Gau{\ss} sums and applications   We present new ideas for computing elliptic Gau{\ss} sums, which constitute
an analogue of the classical cyclotomic Gau{\ss} sums and whose use has been
proposed in the context of counting points on elliptic curves and primality
tests. By means of certain well-known modular functions we define the universal
elliptic Gau{\ss} sums and prove they admit an efficiently computable
representation in terms of the $j$-invariant and another modular function.
After that, we show how this representation can be used for obtaining the
elliptic Gau{\ss} sum associated to an elliptic curve over a finite field
$\mathbb{F}_p$, which may then be employed for counting points or primality
proving.

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The categories of this paper are: funct-an
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The categories of this paper are: atom-ph
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The categories of this paper are: stat
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The categories of this paper are: eess
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The categories of this paper are: quant-ph
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The categories of this paper are: mtrl-th
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The categories of this paper are: q-bio
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The categories of this paper are: hep-lat
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The categories of this paper are: hep-ex
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The categories of this paper are: ao-sci
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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: q-alg
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The categories of this paper are: adap-org
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The categories of this paper are: patt-sol
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The categories of this paper are: q-fin