On the representations of integers by the sextenary quadratic form x^2+y^2+z^2+ 7s^2+7t^2+ 7u^2 and 7-cores

Details On the representations of integers by the sextenary quadratic form x^2+y^2+z^2+ 7s^2+7t^2+ 7u^2 and 7-cores On the representations of integers by the sextenary quadratic form x^2+y^2+z^2+ 7s^2+7t^2+ 7u^2 and 7-cores

2008-04-13

arxiv.org/abs/0804.2038v1

Mathematics

Number Theory

10 pages

Scientific paper

In this paper we derive an explicit formula for the number of representations of an integer by the sextenary form x^2+y^2+z^2+ 7s^2+7t^2+ 7u^2. We establish the following intriguing inequalities 2b(n)>=a_7(n)>=b(n) for n not equal to 0,2,6,16. Here a_7(n) is the number of partitions of n that are 7-cores and b(n) is the number of representations of n+2 by the sextenary form (x ^2+ y ^2+z ^2+ 7s ^2 + 7t ^2+ 7u^2)/8 with x,y,z,s,t and u being odd.

Affiliated with

Also associated with

No associations

Rating

On the representations of integers by the sextenary quadratic form x^2+y^2+z^2+ 7s^2+7t^2+ 7u^2 and 7-cores 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 On the representations of integers by the sextenary quadratic form x^2+y^2+z^2+ 7s^2+7t^2+ 7u^2 and 7-cores, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and On the representations of integers by the sextenary quadratic form x^2+y^2+z^2+ 7s^2+7t^2+ 7u^2 and 7-cores will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-505824