Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Gowers norms of multiplicative functions in progressions on average   Let $\mu$ be the M\"{o}bius function and let $k \geq 1$. We prove that the
Gowers $U^k$-norm of $\mu$ restricted to progressions $\{n \leq X: n\equiv
a_q\pmod{q}\}$ is $o(1)$ on average over $q\leq X^{1/2-\sigma}$ for any $\sigma
> 0$, where $a_q\pmod{q}$ is an arbitrary residue class with $(a_q,q) = 1$.
This generalizes the Bombieri-Vinogradov inequality for $\mu$, which
corresponds to the special case $k=1$.

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The categories of this paper are: solv-int
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The categories of this paper are: patt-sol
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The categories of this paper are: cmp-lg
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The categories of this paper are: hep-th
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The categories of this paper are: bayes-an
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The categories of this paper are: gr-qc
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The categories of this paper are: hep-lat
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The categories of this paper are: alg-geom
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The categories of this paper are: acc-phys
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The categories of this paper are: nlin
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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: ao-sci
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The categories of this paper are: q-fin
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The categories of this paper are: eess
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The categories of this paper are: stat