OFFSET
1,3
COMMENTS
LINKS
Andy Huchala, Table of n, a(n) for n = 1..20000
Andy Huchala, Growth of A363147(n) vs a(n)
F. Hirzebruch, Modulflächen und Modulkurven zur symmetrischen Hilbertschen Modulgruppe, Annales scientifiques de l’É.N.S. 4e série, tome 11, no 1 (1978), p. 101-165. See page 135.
Jürg Kramer, On the linear independence of certain theta-series, Mathematische Annalen 281.2 (1988): 219-228. See page 226.
EXAMPLE
PROG
(Sage)
bound = 100
P = Primes()
p = 2
for i in range(bound):
p = P.next(p)
if p % 4 == 1:
K1.<a> = NumberField(x^2 - p)
K2.<b> = NumberField(x^2 + p)
K3.<c> = NumberField(x^2 + 3*p)
zeta = K1.zeta_function()
h2 = len(K2.class_group())
h3 = len(K3.class_group())
H_plus = int(abs(.49+1/2*zeta(-1)+1/8 * h2 + 1/6*h3))
H = (H_plus+int((p + 19)/24))/2
if H_plus-H>0:
print(H_plus-H)
CROSSREFS
KEYWORD
nonn
AUTHOR
Andy Huchala, May 17 2023
STATUS
approved