Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: New series for powers of $\pi$ and related congruences   Via symbolic computation we deduce 97 new type series for powers of $\pi$
related to Ramanujan-type series. Here are three typical examples:
$$\sum_{k=0}^\infty \frac{P(k) \binom{2k}k\binom{3k}k
\binom{6k}{3k}}{(k+1)(2k-1)(6k-1)(-640320)^{3k}}
  =\frac{18\times557403^3\sqrt{10005}}{5\pi}$$ with \begin{align*}P(k) =
&637379600041024803108 k^2 + 657229991696087780968 k \\&+ 19850391655004126179,
\end{align*} $$\sum_{k=1}^\infty \frac{(3k+1)16^k}{(2k+1)^2k^3\binom{2k}k^3} =
\frac{\pi^2-8}2,$$ and $$\sum_{n=0}^\infty\frac{3n+1}{(-100)^n}
\sum_{k=0}^n{n\choose k}^2T_k(1,25)T_{n-k}(1,25) = \frac{25}{8\pi},$$ where the
generalized central trinomial coefficient $T_k(b,c)$ denotes the coefficient of
$x^k$ in the expansion of $(x^2+bx+c)^k$. We also formulate a general
characterization of rational Ramanujan-type series for $1/\pi$ via congruences,
and pose 117 new conjectural series for powers of $\pi$ via looking for
corresponding congruences. For example, we conjecture that
$$\sum_{k=0}^\infty\frac{39480k+7321}{(-29700)^k}T_k(14,1)T_k(11,-11)^2=\frac{6795\sqrt5}{\pi}.$$
Eighteen of the new series in this paper involve some imaginary quadratic
fields with class number $8$.

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The categories of this paper are: nucl-ex
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The categories of this paper are: chao-dyn
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The categories of this paper are: cond-mat
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The categories of this paper are: chem-ph
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The categories of this paper are: funct-an
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The categories of this paper are: adap-org
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The categories of this paper are: hep-ex
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The categories of this paper are: acc-phys
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The categories of this paper are: physics
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The categories of this paper are: plasm-ph
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The categories of this paper are: bayes-an
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The categories of this paper are: stat
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The categories of this paper are: econ
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The categories of this paper are: quant-ph
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The categories of this paper are: q-fin
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The categories of this paper are: hep-lat