Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: More than five-twelfths of the zeros of $\zeta$ are on the critical line   The second moment of the Riemann zeta-function twisted by a normalized
Dirichlet polynomial with coefficients of the form $(\mu \star \Lambda_1^{\star
k_1} \star \Lambda_2^{\star k_2} \star \cdots \star \Lambda_d^{\star k_d})$ is
computed unconditionally by means of the autocorrelation of ratios of $\zeta$
techniques from Conrey, Farmer, Keating, Rubinstein and Snaith (2005), Conrey,
Farmer and Zirnbauer (2008) as well as Conrey and Snaith (2007). This in turn
allows us to describe the combinatorial process behind the mollification of \[
\zeta(s) + \lambda_1 \frac{\zeta'(s)}{\log T} + \lambda_2
\frac{\zeta''(s)}{\log^2 T} + \cdots + \lambda_d \frac{\zeta^{(d)}(s)}{\log^d
T}, \] where $\zeta^{(k)}$ stands for the $k$th derivative of the Riemann
zeta-function and $\{\lambda_k\}_{k=1}^d$ are real numbers. Improving on recent
results on long mollifiers and sums of Kloosterman sums due to Pratt and Robles
(2017), as an application, we increase the current lower bound of critical
zeros of the Riemann zeta-function to slightly over five-twelfths.

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The categories of this paper are: hep-lat
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The categories of this paper are: q-alg
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The categories of this paper are: acc-phys
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The categories of this paper are: gr-qc
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The categories of this paper are: alg-geom
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The categories of this paper are: comp-gas
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The categories of this paper are: dg-ga
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The categories of this paper are: patt-sol
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The categories of this paper are: nlin
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The categories of this paper are: eess
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The categories of this paper are: chem-ph
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The categories of this paper are: cmp-lg
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The categories of this paper are: math-ph
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The categories of this paper are: supr-con
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The categories of this paper are: quant-ph
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The categories of this paper are: atom-ph