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17 | − 17 ’dır.
16
(17) = ∑ χ(
x=
0
3 2
−2
).
3 2 3 2
k x x x
= ( χ(0− 2 .0)).0 + ( χ(1−2
.1)).1
3 2 3 2
+ ( χ(2− 2 .2)).2 + ( χ(3
−2
.3)).3
3 2 3 2
+ ( χ(4− 2 .4)).4 + ( χ(5−2
.5)).5
3 2 3 2
+ ( χ(6− 2 .6)).6 + ( χ(7−2
.7)).7
3 2 3 2
+ ( χ(8− 2 .8)).8 + ( χ(9−2
.9)).9
3 2 3 2
+ ( χ(10 − 2 .10)).10 + ( χ(11
−2.11)).11
3 2 3 2
+ ( χ(12 − 2 .12)).12 + ( χ(13
−2
.13)).13
3 2 3 2
+ ( χ(14 − 2 .14)).14 + ( χ(15
−2
.15)).15
3 2
+ ( χ(16
−2
.16)).16
k (17) = 0.0 + ( − 1).1+ 0.2 + 1.3 + ( −1).4
+ ( − 1).5 + ( − 1).6 + 1.7 + 1.8 + 1.9
+ 1.10 + ( − 1).11 + ( − 1).12 + ( −1).13
+ 1.14 + 0.15 + ( −1).16
k (17) = 0− 1+ 0+ 3−4−5− 6+ 7+ 8+ 9
+ 10 −11−12− 13+ 14 + 0 −16
=−17
2 3 2
3.3.8 Teorem p ≡ 1(mod 4) bir asal olsun. y ≡ x − n x (mod p)
eğrisi
üzerindeki ( x, y ) rasyonel noktalarının sayısı
toplamına eşittir ve burada
1 ρ(
x)
+ ∑
x∈Fp
3 2
⎧2 , χ(
x − n x)
= 1
⎪
3 2
ρ( x) = ⎨1
, χ(
x − n x)
= 0
⎪
⎩
x − n x =−
3 2
0 , χ(
) 1
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