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Artículo
Estimates for singular multiplicative character sums
(Duke University Press, 2005)
We give some estimates for multiplicative character sums on quasiprojective varieties over finite fields depending on the severity of the singularities of the variety at infinity. We also remove the hypothesis of ...
Artículo
Purity of exponential sums on An
(Kluwer, 2006-03)
We give a purity result for two kinds of exponential sums of the type ∑x∈knψ(f(x)), where k is a finite field of characteristic p and ψ:k→C⋆ is a non-trivial additive character. In the first case, f∈k[x1,…,xn] is a polynomial ...
Artículo
Moment zeta functions for toric Calabi-Yau hypersurfaces
(International Press, 2007)
Moment zeta functions provide a diophantineformulation for the distribution of rational points on afamily of algebraic varieties over finite fields. They also formalgebraic approximations to Dwork’s pp-adic unit rootzeta ...
Artículo
Continuous division of linear differential operators and faithful flatness of D∞X over DX
(Société Mathématique de France, 2004)
In these notes we prove the faithful flatness of the sheaf of infinite order linear differential operators over the sheaf of finite order linear differential operators on a complex analytic manifold. We give the ...
Artículo
Purity of exponential sums on An, II
(De Gruyer, 2007-03)
We give a purity result for exponential sums of the type P x∈kn ψ(f(x)), where k is a finite field of characteristic p, ψ : k → C* is a non-trivial additive character and f ∈ k[x1, . . . , xn] is a polynomial whose highest ...