# Gauss sums over multiplicative subgroups

Hello,

Is anyone here aware of a well-motivated exposition of the Bourgain-Glibichuk-Konyagin estimate for exponential sums (or Gauss sums) over multiplicative subgroups? If any of you has a write-up on the subject, I would be more than glad to have an opportunity to take a look at it.

Thank you very much!

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Well-motivated is in the eye of the beholder, but Ben Green's notes seem to be good.

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Igor, Thanks for this mention. I did try pretty hard with that particular set of notes, though I might change one or two things if I were doing them again. I had some help from Bourgain and Lindenstrauss. –  Ben Green May 17 '12 at 22:30
Thanks for writing the notes! This branch of mathematics is evolving so fast that one really needs a good guide to keep up (or at least not get left too far behind...) –  Igor Rivin May 17 '12 at 23:04

This theorem (and the relevant background material) are covered in Tao and Vu's Additive Combinatorics, see theorem 4.41 there.

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A very readable introduction is Kurlberg's paper - http://www.math.kth.se/~kurlberg/eprints/short_expsum.pdf

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