素数の星空の中から星座を探せ！ #日曜数学会

Constellations in the Gaussian primes

@tsujimotter

http://tsujimotter.info/

# 2016/06/18

Who are you

tsujimotter

Terrence Tao, “The Gaussian Primes Contain Arbitrarily Shaped Constellations”,

arXiv:math/0501314 [math.CO]

http://arxiv.org/abs/math/0501314

Z[ i ] (Shape)

P[ i ]

(Constellation)

1.2

“ ”

i

2i

3i

-i

-2i

-3i

-1 0 1 2 3 4 5

“ ”

-1 0 1 2 3 4 5

-1 0 1 2 3 4 5

“ ”

-1 0 1 2 3 4 5

i

2i

3i

-i

-2i

-3i

5 + 2i

7

3i {1, -1, i, -i } {p, -p, pi, -pi}

p

{1, -1} {p, -p}

p

5+0i-5+0i

0+5i

0-5i

5 + 2i

3i

100+0i-100+0i

0+100i

0-100i

300+0i-300+0i

0+300i

0-300i

Z[ i ] (Shape)

P[ i ]

(Constellation)

1.2

Shape

Shape Constellation

+30

-30

- 5 - 2i - 1 - 4i 1 - 6i 3 - 8i

3 - 10i 7 - 12i 9 - 10i

+100

-100

-70 + 71i 10 + 61i - 10 - 9i

- 20 - 19i - 30 - 29i 30 - 89i

- 50 - 99i

4/21 5/20

+50

-50

-30 + 23i -38 + 7i -2 + 3i 2 - 1i 2 - 5i

- 2 - 5i - 6 - 5i

6

8

10

+300

-300

5/21 6/21

+50

-50

-38 + 23i -44 + 15i -16 + 9i -6 + 5i -2 + 5i

-32 + 3i -26 + 1i - 12 - 7i

{ -30 + 23i, -38 + 7i, -2 + 3i,

2 - 1i, 2 - 5i, - 2 - 5i, - 6 - 5i }

❤

8/24 9/23

+30

-30

-13 + 2i 7 - 2i

- 11 - 6i 7 - 8i

- 21 - 10i - 7 - 10i - 1 - 10i

- 15 - 14i - 19 - 20i

+1200

-1200

http://tsujimotter.info/works/constellation/