Birch and Swinnerton-Dyer Conjecture

1. The Partial Derivative of the Birch and Swinnerton-Dyer
Conjecture
Gregory Prew
2/28/16

2. L(C,s)=c(s-1)r
, r=2, c≠0,
c(s-1)2
, c(s-1)(s-1) then c(s2
-2s+1) thus
c(sr
-rs+1) when r is inserted in for 2.
dL(C,s)= c{(∂L(C,s)/∂r)dr + (∂L(C,s)/∂ds)ds}
dsr
/dr = sr
(lns)
∂L(C,s)/∂r = c(sr
(lns)-(s))
∂L(C,s)/∂s = c((r)s(r-1)
-(r))
dL(C,s) = c{(sr
(lns)-(s))dr + ((r)s(r-1)
-(r))ds}

3. r=2, s=1
dL(C,s) = c{(-1)dr + 0}
=c(-2) + 0