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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

Table of n, a(n) for n=0..55.

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,changed

AUTHOR

Roger L. Bagula, Mar 23 2006

EXTENSIONS

More terms from Jinyuan Wang, Feb 22 2020

STATUS

approved

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Last modified February 26 02:19 EST 2020. Contains 332270 sequences. (Running on oeis4.)