Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Bounds for theta sums in higher rank I   Theta sums are finite exponential sums with a quadratic form in the
oscillatory phase. This paper establishes new upper bounds for theta sums in
the case of smooth and box truncations. This generalises a classic 1977 result
of Fiedler, Jurkat and K\"orner for one-variable theta sums and, in the
multi-variable case, improves previous estimates obtained by Cosentino and
Flaminio in 2015. Key steps in our approach are the automorphic representation
of theta functions and their growth in the cusps of the underlying homogeneous
space.

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The categories of this paper are: cmp-lg
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The categories of this paper are: econ
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The categories of this paper are: patt-sol
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The categories of this paper are: eess
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The categories of this paper are: nucl-th
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The categories of this paper are: bayes-an
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The categories of this paper are: acc-phys
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The categories of this paper are: quant-ph
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The categories of this paper are: dg-ga
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The categories of this paper are: atom-ph
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The categories of this paper are: solv-int
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The categories of this paper are: astro-ph
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The categories of this paper are: q-bio
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The categories of this paper are: nucl-ex
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The categories of this paper are: gr-qc
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The categories of this paper are: hep-ex