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A114857
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Decimal expansion of 0th Gram point.
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3
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1, 7, 8, 4, 5, 5, 9, 9, 5, 4, 0, 4, 1, 0, 8, 6, 0, 8, 1, 6, 8, 2, 6, 3, 3, 8, 4, 1, 2, 5, 1, 9, 0, 9, 7, 0, 3, 5, 6, 9, 3, 2, 8, 7, 4, 3, 3, 6, 9, 6, 4, 5, 2, 3, 9, 2, 1, 1, 8, 1, 1, 4, 8, 5, 9, 4, 8, 1, 6, 8, 7, 0, 0, 9, 2, 0, 1, 6, 0, 9, 5, 2, 1, 1, 7, 5, 1, 3, 4, 0, 4, 0, 8, 4, 8, 8, 2, 0, 8, 6, 7, 6
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OFFSET
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2,2
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LINKS
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EXAMPLE
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17.8455995...
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MATHEMATICA
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First[ RealDigits[t /. FindRoot[ RiemannSiegelTheta[t] == 0, {t, 17}, WorkingPrecision -> 120], 10, 102]] (* Jean-François Alcover, Jun 07 2012 *)
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PROG
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(PARI) g0(n)=2*Pi*exp(1+lambertw((8*n+1)/exp(1)/8)) \\ approximate location of gram(n)
th(t)=arg(gamma(1/4+I*t/2))-log(Pi)*t/2 \\ theta, but off by some integer multiple of 2*Pi
thapprox(t)=log(t/2/Pi)*t/2-t/2-Pi/8+1/48/t-1/5760/t^3
RStheta(t)=my(T=th(t)); (thapprox(t)-T)\/(2*Pi)*2*Pi+T
gram(n)=my(G=g0(n), k=n*Pi); solve(x=G-.003, G+1e-8, RStheta(x)-k)
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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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