Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Explicit estimates for $\zeta(s)$ in the critical strip under the
  Riemann Hypothesis   Assuming the Riemann Hypothesis, we provide effective upper and lower
estimates for $\left|\zeta(s)\right|$ right to the critical line. As an
application we make explicit Titchmarsh's conditional bound for the Mertens
function and Montgomery--Vaughan's conditional bound for the number of $k$-free
numbers.

24
The categories of this paper are: dg-ga
5
The categories of this paper are: gr-qc
14
The categories of this paper are: math-ph
25
The categories of this paper are: patt-sol
16
The categories of this paper are: stat
23
The categories of this paper are: solv-int
36
The categories of this paper are: cmp-lg
3
The categories of this paper are: physics
26
The categories of this paper are: bayes-an
28
The categories of this paper are: alg-geom
22
The categories of this paper are: chao-dyn
35
The categories of this paper are: mtrl-th
10
The categories of this paper are: q-bio
19
The categories of this paper are: eess
12
The categories of this paper are: nucl-th
29
The categories of this paper are: funct-an