Mathematics – General Mathematics
Scientific paper
2009-06-21
Mathematics
General Mathematics
Added Appendix which briefly introduces the basic theory that several multivariable integral polynomials simultaneously repres
Scientific paper
In 1904, Dickson [5] stated a very important conjecture. Now people call it Dickson's conjecture. In 1958, Schinzel and Sierpinski [14] generalized Dickson's conjecture to the higher order integral polynomial case. However, they did not generalize Dickson's conjecture to the multivariable case. In 2006, Green and Tao [13] considered Dickson's conjecture in the multivariable case and gave directly a generalized Hardy-Littlewood estimation. But, the precise Dickson's conjecture in the multivariable case does not seem to have been formulated. In this paper, based on the idea in [15], we will try to complement this and give an equivalent form of Dickson's Conjecture, furthermore, generalize it to the multivariable case or a system of affine-linear forms on $N^k$ . We also give some remarks and evidences on conjectures in [15]. Finally, in Appendix, we briefly introduce the basic theory that several multivariable integral polynomials represent simultaneously prime numbers for infinitely many integral points.
No associations
LandOfFree
Notes on Dickson's Conjecture does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Notes on Dickson's Conjecture, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Notes on Dickson's Conjecture will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-505302