Small prime solutions to cubic Diophantine equations

Details Small prime solutions to cubic Diophantine equations Small prime solutions to cubic Diophantine equations

2006-10-24

arxiv.org/abs/math/0610739v1

Mathematics

Number Theory

MSc. Thesis, Simon Fraser University, Summer 2006. 55 pages including title page and bibliography, uses sfuthesis.sty

Scientific paper

Let a1,..., a9 be non-zero integers and n any integer. Suppose that a1 + ... + a9 = n (mod 2) and (ai, aj) = 1 for 1 <= i < j <= 9. We will prove that (i) if not all of the aj's are of the same sign, then the cubic diagonal equation a1p1^3 + ... + a9p9^3 = n has prime solutions satisfying pj << n^{1/3} + max{|aj|}^{20+ e}; and (ii) if all aj are positive and n >> max{|aj|}^{61+e}, then the cubic diagonal equation a1p1^3 + ... + a9p9^3 = n is soluble in primes pj. This result is motivated from the analogous result for quadratic diagonal equations by S.K.K. Choi and J. Liu. To prove the results we will use the Hardy-Littlewood Circle method, which we will outline. Lastly, we will make a note on some possible generalizations to this particular problem.

Affiliated with

Also associated with

No associations

Rating

Small prime solutions to cubic Diophantine equations 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 Small prime solutions to cubic Diophantine equations, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Small prime solutions to cubic Diophantine equations will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-378577