On exponential sums

Abstract

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 ${\sum }_{x\in F^n}\Psi (T{r}_{F/F_p}(f(x)))$ 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.

Latex 2.09, 15 pages

Cited by in corpus (2)

• Quasirandom Arithmetic Permutations
• Exponential sums on A^n