Do you know any good reference on Weil bounds for character sums over algebraic curves? I prefer references which assume little previous knowledge.
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1$\begingroup$ Possibly useful: math.ethz.ch/~kowalski/ik-ant-exp-sums.pdf $\endgroup$– David WhiteCommented Sep 13, 2011 at 12:25
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1$\begingroup$ 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. $\endgroup$– David WhiteCommented Sep 13, 2011 at 14:25
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$\begingroup$ The link in a comment above points to a PDF of Chapter 11 "Sums over finite fields" from this book: Iwaniec, Henryk; Kowalski, Emmanuel, Analytic number theory, Colloquium Publications. American Mathematical Society 53. Providence, RI: American Mathematical Society (AMS) (ISBN 0-8218-3633-1/hbk). xi, 615 p. (2004). Zbl 1059.11001. $\endgroup$– The AmplitwistCommented Mar 25, 2023 at 11:51
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2 Answers
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Yes, check out Chapter 8 of this paper:
Chen, Xi; Kayal, Neeraj; Wigderson, Avi, Partial derivatives in arithmetic complexity and beyond, Found. Trends Theor. Comput. Sci. 6, No. 1–2, 1–138 (2010). Zbl 1278.68010. PDF
answered Sep 13, 2011 at 12:04
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D. R. Kohel and I. E. Shparlinski, 'On exponential sums and group generators for elliptic curves over finite fields', Lect. Notes in Comp. Sci., Springer-Verlag, Berlin, 1838 (2000), 395–404. Zbl 1032.11034
answered Sep 13, 2011 at 14:01