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Search: id:A116583
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| A116583 |
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A better hermitian prime genus function. |
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1
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| 0, 0, 0, 1, 0, 4, 3, 8, 7, 14, 23, 34, 33, 46, 45, 60, 76, 96, 116, 115, 139, 163, 162, 189, 249, 248, 281, 280, 316, 315, 431, 430, 473, 518, 564, 613, 664, 716, 715, 770, 826, 886, 945, 1009, 1008, 1073, 1208, 1351, 1350, 1426
(list; graph; listen)
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OFFSET
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0,6
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COMMENT
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Better solution with complex structure: ca = (1/Sqrt[2])*(hh + I*gg) cb = (1/Sqrt[2])*(hh - I*gg) Solve[g0 - ca*cb == 0, gg] Result function r[n]: r[n]^(2/5)-->g[n]*Parity[n]
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REFERENCES
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Ken Ono, Scott Ahlgren,Weierstrass points on X0(p) and supersingular j-invariants Mathematiche Annalen 325, 2003, pp. 355-368
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FORMULA
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g[n]=modulo 12 prime genus of n h[n]=modulo 6 prime genus of n Hermitian function: c[n]=(1/Sqrt[2])*(h[n]-I*Sqrt[ -2*g[n]+h[n]^2) cStar[n]=(1/Sqrt[2])*(h[n]+I*Sqrt[ -2*g[n]+h[n]^2) a(n) =c[n]*cStar[n]
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MATHEMATICA
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g[1] = 1; g[2] = 1; g[n_] := (Prime[n] - 13)/12 /; Mod[Prime[n], 12] - 1 == 0 g[n_] := (Prime[n] - 5)/12 /; Mod[Prime[n], 12] - 5 == 0 g[n_] := (Prime[n] - 7)/12 /; Mod[Prime[n], 12] - 7 == 0 g[n_] := (Prime[n] + 1)/12 /; Mod[Prime[n], 12] - 11 == 0 h[1] = 1; h[2] = 1; h[n_] := (Prime[n])/6 /; Mod[Prime[n], 6] == 0 h[n_] := (Prime[n] - 1)/6 /; Mod[Prime[n], 6] - 1 == 0 h[n_] := (Prime[n] - 2)/6 /; Mod[Prime[n], 6] - 2 == 0 h[n_] := (Prime[n] - 3)/6 /; Mod[Prime[n], 6] - 3 == 0 h[n_] := (Prime[n] - 4)/6 /; Mod[Prime[n], 6] - 4 == 0 h[n_] := (Prime[n] - 5)/6 /; Mod[Prime[n], 6] - 5 == 0 c[n_]=(1/Sqrt[2])*(h[n]-I*Sqrt[ -2*g[n]+h[n]^2) cStar[n_]=(1/Sqrt[2])*(h[n]+I*Sqrt[ -2*g[n]+h[n]^2) a = Table[ExpandAll[c[n]*cStar[n]], {n, 1, 50}]
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CROSSREFS
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Sequence in context: A110662 A132021 A089368 this_sequence A134390 A021699 A131416
Adjacent sequences: A116580 A116581 A116582 this_sequence A116584 A116585 A116586
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KEYWORD
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nonn,uned,probation,obsc
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AUTHOR
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Roger Bagula (rlbagulatftn(AT)yahoo.com), Mar 23 2006
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