Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Combining Igusa's conjectures on exponential sums and monodromy with
  semi-continuity of the minimal exponent   We combine two of Igusa's conjectures with recent semi-continuity results by
Musta\c{t}\u{a} and Popa to form a new, simple conjecture on bounds for
exponential sums. These bounds have a formulation in terms of degrees and
dimensions only. We provide evidence for our new question, partly by adapting
already known results about Igusa's conjecture on exponential sums, but also
some new evidence like for polynomials in 4 variables. We show that, in turn,
these bounds imply consequences for Igusa's (strong) monodromy conjecture. The
bounds lead to estimates for major arcs appearing in the circle method towards
local-global principles; if minor arcs would follow this improvement (a huge
challenge), then Birch's local-global principle for polynomials in many
variables for given degree would generalize vastly.

13
The categories of this paper are: quant-ph
35
The categories of this paper are: mtrl-th
8
The categories of this paper are: hep-ex
4
The categories of this paper are: cond-mat
23
The categories of this paper are: solv-int
3
The categories of this paper are: physics
15
The categories of this paper are: nucl-ex
21
The categories of this paper are: adap-org
30
The categories of this paper are: q-alg
5
The categories of this paper are: gr-qc
37
The categories of this paper are: supr-con
12
The categories of this paper are: nucl-th
29
The categories of this paper are: funct-an
24
The categories of this paper are: dg-ga
18
The categories of this paper are: econ
22
The categories of this paper are: chao-dyn