Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Analytic van der Corput Lemma for p-adic and F_q((t)) oscillatory
  integrals, singular Fourier transforms, and restriction theorems   We give the p-adic and F_q((t)) analogue of the real van der Corput Lemma,
where the real condition of sufficient smoothness for the phase is replaced by
the condition that the phase is a convergent power series. This van der Corput
style result allows us, in analogy to the real situation, to study singular
Fourier transforms on suitably curved (analytic) manifolds and opens the way
for further applications. As one such further application we give the
restriction theorem for Fourier transforms of L^p functions to suitably curved
analytic manifolds over non-archimedean local fields, similar to the real
restriction result by E. Stein and C. Fefferman.

26
The categories of this paper are: bayes-an
16
The categories of this paper are: stat
8
The categories of this paper are: hep-ex
9
The categories of this paper are: nlin
37
The categories of this paper are: supr-con
29
The categories of this paper are: funct-an
18
The categories of this paper are: econ
24
The categories of this paper are: dg-ga
11
The categories of this paper are: hep-lat
15
The categories of this paper are: nucl-ex
10
The categories of this paper are: q-bio
3
The categories of this paper are: physics
5
The categories of this paper are: gr-qc
13
The categories of this paper are: quant-ph
35
The categories of this paper are: mtrl-th
21
The categories of this paper are: adap-org