On additive shifts of multiplicative subgroups

Details On additive shifts of multiplicative subgroups On additive shifts of multiplicative subgroups

2011-02-06

arxiv.org/abs/1102.1172v1

Mathematics

Number Theory

18 pages

Scientific paper

Generalizing a result of S.V. Konyagin and D.R. Heath--Brown, we prove, in particular, that for any multiplicative subgroup R of Z/pZ and any nonzero elements mu_1,...,mu_k the following holds |R \cap (R+mu_1) \cap ... \cap (R+mu_k)| \ll_k |R|^{1/2+alpha_k}, provided by 1 \ll_k |R| \ll_k p^{1-\beta_k}, where alpha_k, beta_k are some sequences of positive reals and alpha_k, beta_k tend to zero. Besides we show that for an arbitrary subgroup R, |R| < p^{1/2} one have |R\pm R| > |R|^{5/3} \log^{-1/2} |R|.

Affiliated with

Also associated with

No associations

Rating

On additive shifts of multiplicative subgroups 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 additive shifts of multiplicative subgroups, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and On additive shifts of multiplicative subgroups will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-506385