A116583 A better Hermitian prime genus function.

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

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: A132021 A089368 A357130 * A196521 A021699 A131416

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