On exponential sums

Details On exponential sums On exponential sums

1997-02-06

arxiv.org/abs/alg-geom/9702006v1

Mathematics

Algebraic Geometry

Latex 2.09, 15 pages

Scientific paper

Let f be a polinomial with coefficients in a finite field F. Let $\Psi : F \to C^{\ast}$ be a non-trivial additive character. In this paper we give bounds for the exponential sums $\sum_{x\in F^n} \Psi (Tr_{F/F_p} (f(x)))$ in some cases where the highest degree form of f defines a singular projective hypersurface X (e.g. when X is an arrangement of lines in P^2). The bound involves the Milnor numbers of the singularities of X. The proof goes via the classical cohomological interpretation of this exponential sums through Grothendieck's trace formula.

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