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 A116583 A better Hermitian prime genus function. 0
 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, 1425, 1501, 1581, 1660, 1743, 1827 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,6 LINKS Ken Ono and Scott Ahlgren, Weierstrass points on X0(p) and supersingular j-invariants, Mathematische Annalen 325, 2003, pp. 355-368. MATHEMATICA 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]) Table[ExpandAll[c[n]*cStar[n]], {n, 1, 50}] (* Slightly modified by Jinyuan Wang, Feb 22 2020 *) CROSSREFS Sequence in context: A302258 A132021 A089368 * A196521 A134390 A021699 Adjacent sequences:  A116580 A116581 A116582 * A116584 A116585 A116586 KEYWORD nonn,uned,obsc AUTHOR Roger L. Bagula, Mar 23 2006 EXTENSIONS More terms from Jinyuan Wang, Feb 22 2020 STATUS approved

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Last modified August 18 02:34 EDT 2022. Contains 356204 sequences. (Running on oeis4.)