The document contains mathematical equations and discussions involving prime numbers, polynomials, and Heegner numbers. It explores properties of prime-generating polynomials and uses formulas to calculate values of eπ√d for different values of d, relating these to class numbers of imaginary quadratic fields. Bounds on Heegner numbers d are derived based on results from Heilbronn and Linfoot.
10. Q(
p
-5), Q(
p
-6), Q(
p
-10), Q(
p
-13), Q(
p
-14), Q(
p
-15)
Q(
p
-15), Q(
p
-17), Q(
p
-21), Q(
p
-22), Q(
p
-23), · · ·
Q(
p
-1), Q(
p
-2), Q(
p
-3), Q(
p
-7), Q(
p
-11), Q(
p
-19), Q
Q(
p
-7), Q(
p
-11), Q(
p
-19), Q(
p
-43), Q(
p
-67), Q(
p
-163)
33. Heegner Number
Q(
p
-d) Heegner Number h log " - 32
21 ⇡
p
d < e
⇡
p
d
100
h0
log "0
- 80
33 ⇡
p
d < e
⇡
p
d
100
---- (1)
---- (2)
(1), (2) |b log " + b0
log "0
| < e- B
B <
⇣
4n2
-1
l2n
log A
⌘(2n+1)2
< 10250
⇣
B = 140
p
d
⌘
) d < 10500
(A)
34. Heegner Number
Heilbronn, Linfoot
10 Heegner Number d > e1000000
(B)
d
(B)(A)
d > e1000000) d < 10500
d (QED)
tsujimotter
http://tsujimotter.hatenablog.com/entry/class-numbers-of-imaginary-quadratic-fields