Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The Explicit Formula and a Propagator   I give a new derivation of the Explicit Formula for the general number field
K, which treats all primes in exactly the same way, whether they are discrete
or archimedean, and also ramified or not. In another token, I advance a
probabilistic interpretation of Weil's positivity criterion, as opposed to the
usual geometrical analogies or goals. But in the end, I argue that the new
formulation of the Explicit Formula signals a specific link with Quantum
Fields, as opposed to the Hilbert-Polya operator idea (which leads rather to
Quantum Mechanics).

10
The categories of this paper are: q-bio
37
The categories of this paper are: supr-con
18
The categories of this paper are: econ
15
The categories of this paper are: nucl-ex
23
The categories of this paper are: solv-int
28
The categories of this paper are: alg-geom
7
The categories of this paper are: hep-th
33
The categories of this paper are: plasm-ph
17
The categories of this paper are: q-fin
1
The categories of this paper are: cs
20
The categories of this paper are: acc-phys
0
The categories of this paper are: hep-ph
12
The categories of this paper are: nucl-th
35
The categories of this paper are: mtrl-th
5
The categories of this paper are: gr-qc
30
The categories of this paper are: q-alg