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Do you know on any good reference on Weil bound for charcter sums over algebraic curves. I prefer reference which assume few previous knowlage.

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Possibly useful: math.ethz.ch/~kowalski/ik-ant-exp-sums.pdf –  David White Sep 13 '11 at 12:25
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I did some retagging, mainly because this was already on the front page. The two answers so far are both lecture notes or textbooks, and I suspect you're going to get mostly textbook type answers because you want it to assume little background. –  David White Sep 13 '11 at 14:25
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up vote 1 down vote accepted

Yes, check out this paper:

http://www.math.ias.edu/~avi/PUBLICATIONS/MYPAPERS/CKW11/CKW11.pdf

Chapter 8.

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D. R. Kohel and I. E. Shparlinski, `Exponential sums and group generators for elliptic curves over finite fields', Lect. Notes in Comp. Sci., Springer-Verlag, Berlin, 1838 (2000), 395--404.

http://www.springerlink.com/content/l37555215161761t/

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