Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The Erdos discrepancy problem   We show that for any sequence $f: {\bf N} \to \{-1,+1\}$ taking values in
$\{-1,+1\}$, the discrepancy $$ \sup_{n,d \in {\bf N}} \left|\sum_{j=1}^n
f(jd)\right| $$ of $f$ is infinite. This answers a question of Erd\H{o}s. In
fact the argument also applies to sequences $f$ taking values in the unit
sphere of a real or complex Hilbert space.
  The argument uses three ingredients. The first is a Fourier-analytic
reduction, obtained as part of the Polymath5 project on this problem, which
reduces the problem to the case when $f$ is replaced by a (stochastic)
completely multiplicative function ${\bf g}$. The second is a logarithmically
averaged version of the Elliott conjecture, established recently by the author,
which effectively reduces to the case when ${\bf g}$ usually pretends to be a
modulated Dirichlet character. The final ingredient is (an extension of) a
further argument obtained by the Polymath5 project which shows unbounded
discrepancy in this case.

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The categories of this paper are: hep-lat
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The categories of this paper are: bayes-an
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The categories of this paper are: patt-sol
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The categories of this paper are: chao-dyn
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The categories of this paper are: math-ph
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The categories of this paper are: mtrl-th
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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: q-fin
0
The categories of this paper are: hep-ph
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The categories of this paper are: hep-ex
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The categories of this paper are: chem-ph
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The categories of this paper are: acc-phys
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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: cs