Constellations in $Bbb P^n$












2














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







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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
















2














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







share|cite|improve this question
























  • 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














2












2








2







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







share|cite|improve this question















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






share|cite|improve this question















share|cite|improve this question













share|cite|improve this question




share|cite|improve this question








edited Nov 28 at 14:35









amWhy

191k28224439




191k28224439










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


















  • 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










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.






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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.






    share|cite|improve this answer


























      2














      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.






      share|cite|improve this answer
























        2












        2








        2






        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.






        share|cite|improve this answer












        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.







        share|cite|improve this answer












        share|cite|improve this answer



        share|cite|improve this answer










        answered Dec 10 '14 at 17:38









        Charles

        23.7k451113




        23.7k451113






























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