On Sumsets and Spectral Gaps

Details On Sumsets and Spectral Gaps On Sumsets and Spectral Gaps

2007-08-02

arxiv.org/abs/0708.0381v3

Mathematics

Combinatorics

A few typos have been corrected. Also theorem 2 in the last draft should have said ``t >= 3'', not ``t >= 2''

Scientific paper

It is well known that if S is a subset of the integers mod p, and if the second-largest Fourier coefficient is ``small'' relative to the largest coefficient, then the sumset S+S is much larger than S. We show in the present paper that if instead of having such a large ``spectral gap'' between the largest and second-largest Fourier coefficients, we had it between the kth largest and the (k+1)st largest, the same thing holds true, namely that |S+S| is appreciably larger than |S|. Well, we only do this for k < (log p)/(log 4). We also obtain analogous results for repeated sumsets S+S+...+S, and it turns out that the more terms one includes, the larger the index k that can be used.

Affiliated with

Also associated with

No associations

Rating

On Sumsets and Spectral Gaps 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 Sumsets and Spectral Gaps, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and On Sumsets and Spectral Gaps will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-245277