Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Toward verification of the Riemann hypothesis: Application of the Li
  criterion   We substantially apply the Li criterion for the Riemann hypothesis to hold.
Based upon a series representation for the sequence \{\lambda_k\}, which are
certain logarithmic derivatives of the Riemann xi function evaluated at unity,
we determine new bounds for relevant Riemann zeta function sums and the
sequence itself. We find that the Riemann hypothesis holds if certain
conjectured properties of a sequence \eta_j are valid. The constants \eta_j
enter the Laurent expansion of the logarithmic derivative of the zeta function
about s=1 and appear to have remarkable characteristics. {\em On our
conjecture}, not only does the Riemann hypothesis follow, but an inequality
governing the values \lambda_n and inequalities for the sums of reciprocal
powers of the nontrivial zeros of the zeta function.

8
The categories of this paper are: hep-ex
13
The categories of this paper are: quant-ph
5
The categories of this paper are: gr-qc
11
The categories of this paper are: hep-lat
27
The categories of this paper are: comp-gas
23
The categories of this paper are: solv-int
3
The categories of this paper are: physics
29
The categories of this paper are: funct-an
31
The categories of this paper are: ao-sci
19
The categories of this paper are: eess
35
The categories of this paper are: mtrl-th
30
The categories of this paper are: q-alg
4
The categories of this paper are: cond-mat
17
The categories of this paper are: q-fin
21
The categories of this paper are: adap-org
36
The categories of this paper are: cmp-lg