Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Moments and oscillations of exponential sums related to cusp forms   We consider large values of long linear exponential sums involving Fourier
coefficients of holomorphic cusp forms. The sums we consider involve rational
linear twists $e(nh/k)$ with sufficiently small denominators. We prove both
pointwise upper bounds and bounds for the frequency of large values. In
particular, the $k$-aspect is treated. As an application we obtain upper bounds
for all the moments of the sums in question. We also give the asymptotics with
the right main term for fourth moments.
  We also consider the mean square of very short sums, proving that on average
short linear sums with rational additive twists exhibit square root
cancellation. This result is also proved in a slightly sharper form.
  Finally, the consideration of moment estimates for both long and short
exponential sums culminates in a result concerning the oscillation of the long
linear sums. Essentially, this result says that for a positive proportion of
time, such a sum stays in fairly long intervals, where its order of magnitude
does not drop below the average order of magnitude and where its argument is in
a given interval of length $3\pi/2+\varepsilon$ and so can not wind around the
origin.

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The categories of this paper are: dg-ga
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The categories of this paper are: funct-an
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The categories of this paper are: chem-ph
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The categories of this paper are: nucl-th
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The categories of this paper are: alg-geom
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The categories of this paper are: cond-mat
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The categories of this paper are: acc-phys
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The categories of this paper are: supr-con
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The categories of this paper are: hep-lat
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The categories of this paper are: econ
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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: adap-org
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The categories of this paper are: astro-ph
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The categories of this paper are: q-fin
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The categories of this paper are: plasm-ph