Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Counting Prime $k$-tuples   Exact summatory functions that count the number of prime $k$-tuples up to
some cut-off integer are presented. Related summatory $k$-tuple analogs of the
first and second Chebyshev functions are then defined. Using a gamma
distribution hypothesis for prime powers, associated average summatory
functions are conjectured. With exact and average summatory functions in hand,
pertinent $k$-tuple zeta functions can be identified, and Perron's formula
allows the formulation of $k$-tuple analogs of explicit formulae. The $k$-tuple
zeta functions are then used to make some inferences about $k$-tuple primes.

4
The categories of this paper are: cond-mat
18
The categories of this paper are: econ
25
The categories of this paper are: patt-sol
12
The categories of this paper are: nucl-th
35
The categories of this paper are: mtrl-th
11
The categories of this paper are: hep-lat
15
The categories of this paper are: nucl-ex
33
The categories of this paper are: plasm-ph
17
The categories of this paper are: q-fin
24
The categories of this paper are: dg-ga
23
The categories of this paper are: solv-int
36
The categories of this paper are: cmp-lg
13
The categories of this paper are: quant-ph
32
The categories of this paper are: atom-ph
3
The categories of this paper are: physics
14
The categories of this paper are: math-ph