Dickson's conjecture on $Z^n$--An equivalent form of Green-Tao's conjecture

Shaohua Zhang

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arXiv · 0911.3679

Dickson's conjecture on $Z^n$--An equivalent form of Green-Tao's conjecture

Shaohua Zhang

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Abstract

In [1], we give Dickson's conjecture on $N^n$. In this paper, we further give Dickson's conjecture on $Z^n$ and obtain an equivalent form of Green-Tao's conjecture [2]. Based on our work, it is possible to establish a general theory that several multivariable integral polynomials on $Z^n$ represent simultaneously prime numbers for infinitely many integral points and generalize the analogy of Chinese Remainder Theorem in [3]. Dans [1], nous donnons la conjecture de Dickson sur $N^n$. Dans ce document, en outre nous accordons une conjecture de Dickson sur $Z^n$ et obtenons une forme équivalent de conjecture de Green-Tao [2]. Sur la base de nos travaux, il est possible d'établir une théorie générale que plusieurs polynômes intégraux multivariables sur $Z^n$ représentent simultanément les nombres premiers pour un nombre infini de points entiers et de généraliser les l'analogie de Théorème des Restes Chinois dans [3].

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Shaohua Zhang. 2009-11-19. Dickson's conjecture on $Z^n$--An equivalent form of Green-Tao's conjecture. https://arxiv.org/abs/0911.3679

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