Multiple Integration of the Birch and Swinnerton-Dyer shirt

1. Multiple Integration of The Birch and
Swinnerton-Dyer Conjecture
5/27/2015
Gregory Prew
L(C,s)=c(s-1)r
, r=2 & c≠0,
thus c(s-1)(s-1), therefore, c(s2
-2s+1) , hence,
c(sr
-rs+1), when r is inserted in for 2.
∫∫L(C,s) = c (∫∫sr
drds-∫∫rs drds +1∫∫drds) + C
∫sr
dr = sr
/ln(s) + C

2. b
|sb
/ln(s)-sa
/ln(s) = (sb
-sa
)/ln(s)
a
d
|d(r+1)
/(r+1)- c(r+1)
/(r+1)= (d(r+1)
-c(r+1)
)/(r+1)
c
c{((sb
-sa
)/ln(s))((d(r+1)
-c(r+1)
)/(r+1)) - ∫∫ rs drds
+1∫∫drds}+C
b
s∫∫rdrds= | (b2
/2-a2
/2) = s(b2
/2-a2
/2)
a
d
r∫∫sdrds= | (d2
/2-c2
/2)= r(d2
/2-c2
/2)
c

3. +1∫∫drds=(b-a)(d-c)+C
Soln.:
a=1, b=2,c=3,d=4,s=1,&r=2
c{((sb
-sa
)/ln(s))((d(r+1)
-c(r+1)
)/(r+1))-(s(b2
/2-a2
/2))(r(d2
/2-
c2
/2))+(b-a)(d-c)} + C
c{(12
-11
)/ ln(1))((4(2+1)
-3(2+1)
)/(2+1))- (1(22
/2-12
/2))
(2(42
/2-32
/2))+(2-1)(4-3)}+ C
c{-(3/2)[2(16/2-9/2)] + 1} +C
c{-(3/2)[7] +1}+C

4. c{-21/2 +1} + C
c{-21/2+2/2} +C
c{-19/2} + C