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A225962
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Decimal expansion of a minimum of Arias de Reyna and van de Lune's kappa function.
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1
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6, 7, 0, 2, 5, 9, 7, 9, 8, 7, 6, 8, 5, 9, 9, 5, 0, 2, 8, 8, 3, 9, 1, 6, 4, 1, 1, 9, 6, 8, 6, 6, 7, 4, 4, 7, 4, 8, 0, 3, 9, 2, 7, 9, 0, 0, 9, 7, 4, 3, 4, 9, 1, 7, 3
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OFFSET
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0,1
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COMMENTS
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The kappa function is implicitly defined by exp(2*Pi*i*kappa(t)) = -exp(-2*i*theta(t))*(zeta'(1/2-i*t)/zeta'(1/2+i*t)) and kappa(0)=-1/2.
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LINKS
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EXAMPLE
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-0.6702597987685995028839164119686674474803927900974349173...
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MATHEMATICA
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kappa[t_] := -1 - 1/Pi* Arg[ RiemannSiegelZ'[t] - I*RiemannSiegelZ[t]*RiemannSiegelTheta'[t]]; digits = 55; kappa0[n_] := kappa0[n] = FindMinimum[kappa[t], {t, 1}, WorkingPrecision -> n] [[1]] // RealDigits[#, 10, digits] & // First; kappa0[digits]; kappa0[n = 2*digits]; While[ kappa0[n] != kappa0[n - digits], n = n + digits]; kappa0[n]
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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