Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On iterated product sets with shifts   We prove that, for any finite set $A \subset \mathbb Q$ with $|AA| \leq K|A|$
and any positive integer $k$, the $k$-fold product set of the shift $A+1$
satisfies the bound $$| \{(a_1+1)(a_2+1) \cdots (a_k+1) : a_i \in A \}| \geq
\frac{|A|^k}{(8k^4)^{kK}}. $$ This result is essentially optimal when $K$ is of
the order $c\log|A|$, for a sufficiently small constant $c=c(k)$.
  Our main tool is a multiplicative variant of the $\Lambda$-constants used in
harmonic analysis, applied to Dirichlet polynomials.

14
The categories of this paper are: math-ph
4
The categories of this paper are: cond-mat
27
The categories of this paper are: comp-gas
6
The categories of this paper are: astro-ph
36
The categories of this paper are: cmp-lg
25
The categories of this paper are: patt-sol
21
The categories of this paper are: adap-org
22
The categories of this paper are: chao-dyn
18
The categories of this paper are: econ
9
The categories of this paper are: nlin
30
The categories of this paper are: q-alg
15
The categories of this paper are: nucl-ex
23
The categories of this paper are: solv-int
17
The categories of this paper are: q-fin
32
The categories of this paper are: atom-ph
7
The categories of this paper are: hep-th