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Some new series for $1/\pi$ and related congruences

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arxiv 1104.3856 v9 pith:XINMDVGA submitted 2011-04-19 math.NT math.CAmath.CO

classification math.NTmath.CAmath.CO
keywords congruencesrelatedseriessomebinaryconjecturalformsinvolving
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abstract

In this paper we prove some new series for $1/\pi$ as well as related congruences. We also raise several new kinds of series for $1/\pi$ and present some related conjectural congruences involving representations of primes by binary quadratic forms.

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Cited by 1 Pith paper

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  1. Eulers Horizonte -- M\"oglichkeiten und Grenzen seiner Arbeitsweise in der Mathematik

    math.HO 2025-05 conditional novelty 4.0 of 10

    A documented account of how Euler worked, what he anticipated, where he erred, and what his methods could not achieve, with several new derivations from his formulas.

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