Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On two Diophantine inequalities over primes (II)   Let $1<c<\frac{26088036}{12301745},c\not=2$ and $N$ be a sufficiently large
real number. In this paper, it is proved that, for almost all $R\in (N,2N]$,
the Diophantine inequality \begin{equation*}
  \big|p_1^c+p_2^c+p_3^c-R\big|<\log^{-1}N \end{equation*} is solvable in
primes $p_1,p_2,p_3$. Moreover, we also prove that the following Diophantine
inequality \begin{equation*}
  \big|p_1^c+p_2^c+p_3^c+p_4^c+p_5^c+p_6^c-N\big|<\log^{-1}N \end{equation*} is
solvable in prime variables $p_1,p_2,p_3,p_4,p_5,p_6$, which improves the
previous result $1<c<\frac{37}{18},c\neq2$.

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The categories of this paper are: funct-an
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The categories of this paper are: mtrl-th
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The categories of this paper are: gr-qc
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The categories of this paper are: hep-ph
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The categories of this paper are: bayes-an
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The categories of this paper are: physics
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The categories of this paper are: q-alg
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The categories of this paper are: adap-org
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The categories of this paper are: chao-dyn
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The categories of this paper are: econ
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The categories of this paper are: nucl-ex
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The categories of this paper are: hep-lat
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The categories of this paper are: hep-ex
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The categories of this paper are: comp-gas
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The categories of this paper are: nucl-th
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The categories of this paper are: math-ph