際際滷

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The Partial Derivative of the Birch and Swinnerton-Dyer
Conjecture
Gregory Prew
2/28/16
L(C,s)=c(s-1)r
, r=2, c0,
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}
r=2, s=1
dL(C,s) = c{(-1)dr + 0}
=c(-2) + 0

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Partial derivative

  • 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, c0, 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