منابع مشابه
Estimates for “Singular” Exponential Sums
In [D1, Thm. 8.4], Deligne proved the following beautiful estimate for exponential sums in n ≥ 1 variables. Given a polynomial f(x1, . . . , xn) in n variables over k of some degree d ≥ 1, write it as f = Fd + Fd−1 + · · · F0 with Fi homogeneous of degree i. Suppose that the following two conditions are satisfied. (1) The degree d is prime to p := char(k). (2) The locus Fd = 0 is a nonsingular ...
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where the sum is taken over a complete set of residues for x modulo q and eq(t) = e2πit/q. The study of these sums is readily motivated by applications in analytic number theory and elsewhere. The first important estimates for sums in one variable appear in the work of Weyl (1916) on uniform distribution. This led to van der Corput’s method with applications to the zeta function, the divisor pr...
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We prove some improvements of the classical Weil bound for one variable additive and multiplicative character sums associated to a polynomial over a finite field k = Fq for two classes of polynomials which are invariant under a large abelian group of automorphisms of the affine line Ak: those invariant under translation by elements of k and those invariant under homotheties with ratios in a lar...
متن کاملDiophantineMethods for Exponential Sums, and Exponential Sums for Diophantine Problems
Recent developments in the theory and application of the HardyLittlewood method are discussed, concentrating on aspects associated with diagonal diophantine problems. Recent efficient differencing methods for estimating mean values of exponential sums are described first, concentrating on developments involving smooth Weyl sums. Next, arithmetic variants of classical inequalities of Bessel and ...
متن کاملNew estimates of double trigonometric sums with exponential functions
We establish a new bound for the exponential sum x∈X y∈Y γ(y) exp(2πiaλ xy /p) , where λ is an element of the residue ring modulo a large prime number p, X and Y are arbitrary subsets of the residue ring modulo p − 1 and γ(n) are any complex numbers with |γ(n)| ≤ 1. In particular, we improve several previously known bounds.
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 1980
ISSN: 0002-9939
DOI: 10.1090/s0002-9939-1980-0567973-5