Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: An Unconditional large gap between the Zeros of the Riemann
  Zeta-Function and Existence of Conditional Large Gaps   In this paper, we prove the lower bound of the unconditional large gap is
3.5555 which improves the obtained value 3.079 in the literature. Next, on the
hypothesis that the moments of the Hardy Z-function and its derivatives are
correctly predicted we establish a new explicit formula of the gaps and use it
to establish some lower bounds for k=3,4,...,15. In particular it is proved
that lower bound when k=15 is 9.6435 which means that the consecutive
nontrivial zeros often differ by at least 9.6435 times the average spacing. The
main results are proved by employed an integral inequality with a best constant
proved by David Boyd.

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The categories of this paper are: patt-sol
15
The categories of this paper are: nucl-ex
26
The categories of this paper are: bayes-an
14
The categories of this paper are: math-ph
20
The categories of this paper are: acc-phys
7
The categories of this paper are: hep-th
1
The categories of this paper are: cs
27
The categories of this paper are: comp-gas
24
The categories of this paper are: dg-ga
18
The categories of this paper are: econ
31
The categories of this paper are: ao-sci
19
The categories of this paper are: eess
28
The categories of this paper are: alg-geom
8
The categories of this paper are: hep-ex
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The categories of this paper are: cmp-lg
10
The categories of this paper are: q-bio