Constellations in $Bbb P^n$
In one of his papers, Tao shows that set of Gaussian primes $Bbb P[i]$ contains arbitrarily shaped constellations (where "shape" is any set of Gaussian integers and "constellation" of that shape is scaled and translated version of it).
I'm almost sure that I have seen the similar claim involving Cartestian product of set of (real) primes with itself, i.e. $Bbb P^n$. However, I don't seem to be able to find any reference for that, and such reference is what I'm asking for. I might have also seen this as a conjecture somewhere.
Thanks in advance.
reference-request prime-numbers
edited Nov 28 at 14:35
amWhy
191k28224439
asked Dec 9 '14 at 21:33
Wojowu
16.9k22564
add a comment |
In one of his papers, Tao shows that set of Gaussian primes $Bbb P[i]$ contains arbitrarily shaped constellations (where "shape" is any set of Gaussian integers and "constellation" of that shape is scaled and translated version of it).
I'm almost sure that I have seen the similar claim involving Cartestian product of set of (real) primes with itself, i.e. $Bbb P^n$. However, I don't seem to be able to find any reference for that, and such reference is what I'm asking for. I might have also seen this as a conjecture somewhere.
Thanks in advance.
reference-request prime-numbers
edited Nov 28 at 14:35
amWhy
191k28224439
asked Dec 9 '14 at 21:33
Wojowu
16.9k22564
Can you please post a reference to the Tao paper?
– Klangen
Nov 28 at 14:27
1
@Flermat arxiv.org/abs/math/0501314
– Wojowu
Nov 28 at 14:37
Thank you for the link.
– Klangen
Nov 28 at 14:39
add a comment |
In one of his papers, Tao shows that set of Gaussian primes $Bbb P[i]$ contains arbitrarily shaped constellations (where "shape" is any set of Gaussian integers and "constellation" of that shape is scaled and translated version of it).
I'm almost sure that I have seen the similar claim involving Cartestian product of set of (real) primes with itself, i.e. $Bbb P^n$. However, I don't seem to be able to find any reference for that, and such reference is what I'm asking for. I might have also seen this as a conjecture somewhere.
Thanks in advance.
reference-request prime-numbers
edited Nov 28 at 14:35
amWhy
191k28224439
asked Dec 9 '14 at 21:33
Wojowu
16.9k22564
In one of his papers, Tao shows that set of Gaussian primes $Bbb P[i]$ contains arbitrarily shaped constellations (where "shape" is any set of Gaussian integers and "constellation" of that shape is scaled and translated version of it).
I'm almost sure that I have seen the similar claim involving Cartestian product of set of (real) primes with itself, i.e. $Bbb P^n$. However, I don't seem to be able to find any reference for that, and such reference is what I'm asking for. I might have also seen this as a conjecture somewhere.
Thanks in advance.
reference-request prime-numbers
reference-request prime-numbers
edited Nov 28 at 14:35
amWhy
191k28224439
asked Dec 9 '14 at 21:33
Wojowu
16.9k22564
edited Nov 28 at 14:35
amWhy
191k28224439
asked Dec 9 '14 at 21:33
Wojowu
16.9k22564
edited Nov 28 at 14:35
amWhy
191k28224439
edited Nov 28 at 14:35
amWhy
191k28224439
edited Nov 28 at 14:35
amWhy
191k28224439
191k28224439
asked Dec 9 '14 at 21:33
Wojowu
16.9k22564
asked Dec 9 '14 at 21:33
Wojowu
16.9k22564
asked Dec 9 '14 at 21:33
Wojowu
16.9k22564
16.9k22564
Can you please post a reference to the Tao paper?
– Klangen
Nov 28 at 14:27
1
@Flermat arxiv.org/abs/math/0501314
– Wojowu
Nov 28 at 14:37
Thank you for the link.
– Klangen
Nov 28 at 14:39
add a comment |
Can you please post a reference to the Tao paper?
– Klangen
Nov 28 at 14:27
1
@Flermat arxiv.org/abs/math/0501314
– Wojowu
Nov 28 at 14:37
Thank you for the link.
– Klangen
Nov 28 at 14:39
Can you please post a reference to the Tao paper?
– Klangen
Nov 28 at 14:27
Can you please post a reference to the Tao paper?
– Klangen
Nov 28 at 14:27
1
1
@Flermat arxiv.org/abs/math/0501314
– Wojowu
Nov 28 at 14:37
@Flermat arxiv.org/abs/math/0501314
– Wojowu
Nov 28 at 14:37
Thank you for the link.
– Klangen
Nov 28 at 14:39
Thank you for the link.
– Klangen
Nov 28 at 14:39
add a comment |
1 Answer
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If you can scale and translate a collection $(a_1,b_1),ldots,(a_k,b_k)$ to $(Aa_1+alpha,Bb_1+beta),ldots,(Aa_k+alpha,Bb_k+beta)$, asking for all of the latter to be pairs of primes, then the $a_i$ and $b_i$ are entirely independent—it's no different from the one-dimensional problem. So I would credit this conjecture to Dickson.
answered Dec 10 '14 at 17:38
Charles
23.7k451113
add a comment |
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If you can scale and translate a collection $(a_1,b_1),ldots,(a_k,b_k)$ to $(Aa_1+alpha,Bb_1+beta),ldots,(Aa_k+alpha,Bb_k+beta)$, asking for all of the latter to be pairs of primes, then the $a_i$ and $b_i$ are entirely independent—it's no different from the one-dimensional problem. So I would credit this conjecture to Dickson.
answered Dec 10 '14 at 17:38
Charles
23.7k451113
add a comment |
If you can scale and translate a collection $(a_1,b_1),ldots,(a_k,b_k)$ to $(Aa_1+alpha,Bb_1+beta),ldots,(Aa_k+alpha,Bb_k+beta)$, asking for all of the latter to be pairs of primes, then the $a_i$ and $b_i$ are entirely independent—it's no different from the one-dimensional problem. So I would credit this conjecture to Dickson.
answered Dec 10 '14 at 17:38
Charles
23.7k451113
add a comment |
If you can scale and translate a collection $(a_1,b_1),ldots,(a_k,b_k)$ to $(Aa_1+alpha,Bb_1+beta),ldots,(Aa_k+alpha,Bb_k+beta)$, asking for all of the latter to be pairs of primes, then the $a_i$ and $b_i$ are entirely independent—it's no different from the one-dimensional problem. So I would credit this conjecture to Dickson.
answered Dec 10 '14 at 17:38
Charles
23.7k451113
If you can scale and translate a collection $(a_1,b_1),ldots,(a_k,b_k)$ to $(Aa_1+alpha,Bb_1+beta),ldots,(Aa_k+alpha,Bb_k+beta)$, asking for all of the latter to be pairs of primes, then the $a_i$ and $b_i$ are entirely independent—it's no different from the one-dimensional problem. So I would credit this conjecture to Dickson.
answered Dec 10 '14 at 17:38
Charles
23.7k451113
answered Dec 10 '14 at 17:38
Charles
23.7k451113
answered Dec 10 '14 at 17:38
Charles
23.7k451113
answered Dec 10 '14 at 17:38
Charles
23.7k451113
23.7k451113
add a comment |
add a comment |
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Can you please post a reference to the Tao paper?
– Klangen
Nov 28 at 14:27
1
@Flermat arxiv.org/abs/math/0501314
– Wojowu
Nov 28 at 14:37
Thank you for the link.
– Klangen
Nov 28 at 14:39