Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The supremum of autoconvolutions, with applications to additive number
  theory   We adapt a number-theoretic technique of Yu to prove a purely analytic
theorem: if f(x) is in L^1 and L^2, is nonnegative, and is supported on an
interval of length I, then the supremum of the convolution f*f is at least
0.631 \| f \|_1^2 / I. This improves the previous bound of 0.591389 \| f \|_1^2
/ I. Consequently, we improve the known bounds on several related
number-theoretic problems. For a subset A of {1,2, ..., n}, let g be the
maximum multiplicity of any element of the multiset {a+b: a,b in A}. Our main
corollary is the inequality gn>0.631|A|^2, which holds uniformly for all g, n,
and A.

15
The categories of this paper are: nucl-ex
23
The categories of this paper are: solv-int
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The categories of this paper are: dg-ga
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The categories of this paper are: quant-ph
9
The categories of this paper are: nlin
34
The categories of this paper are: chem-ph
27
The categories of this paper are: comp-gas
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The categories of this paper are: funct-an
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The categories of this paper are: chao-dyn
3
The categories of this paper are: physics
25
The categories of this paper are: patt-sol
28
The categories of this paper are: alg-geom
37
The categories of this paper are: supr-con
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The categories of this paper are: ao-sci
36
The categories of this paper are: cmp-lg
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The categories of this paper are: eess