On some exponential sums with exponential and rational functions
نویسندگان
چکیده
منابع مشابه
Bilinear Sums with Exponential Functions
Let g = 0,±1 be a fixed integer. Given two sequences of complex numbers (φm) ∞ m=1 and (ψn) ∞ n=1 and two sufficiently large integers M and N , we estimate the exponential sums ∑ p≤M gcd(ag,p)=1 ∑ 1≤n≤N φpψnep (ag ) , a ∈ Z, where the outer summation is taken over all primes p ≤ M with gcd(ag, p) = 1.
متن کاملUsing Stepanov’s Method for Exponential Sums Involving Rational Functions
For a non-trivial additive character ψ and multiplicative character χ on a finite field Fq , and rational functions f, g in Fq(x), we show that the elementary Stepanov-Schmidt method can be used to obtain the corresponding Weil bound for the sum ∑ x∈Fq\S χ(g(x))ψ(f(x)) where S is the set of the poles of f and g. We also determine precisely the number of characteristic values ωi of modulus q1/2 ...
متن کاملOn Approximation of Functions by Exponential Sums
We introduce a new approach, and associated algorithms, for the efficient approximation of functions and sequences by short linear combinations of exponential functions with complex-valued exponents and coefficients. These approximations are obtained for a finite but arbitrary accuracy and typically have significantly fewer terms than Fourier representations. We present several examples of thes...
متن کاملOn some congruence with application to exponential sums
We will study the solution of a congruence, x ≡ g(1/2)ωg(2 n) mod 2n, depending on the integers g and n, where ωg(2) denotes the order of g modulo 2n. Moreover, we introduce an application of the above result to the study of an estimation of exponential sums.
متن کاملExponential Sums On
where f (j) is homogeneous of degree j. Theorem 1.4. Suppose (p, δ) = 1 and f (δ) = 0 defines a smooth hypersurface in P. Then L(A, f ; t) n+1 is a polynomial of degree (δ − 1), all of whose reciprocal roots have absolute value q. For exponential sums on A, several generalizations of Deligne’s result have been proved ([1, 2, 5, 7]). In all these theorems, the hypothesis implies that f , regarde...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Rocky Mountain Journal of Mathematics
سال: 2013
ISSN: 0035-7596
DOI: 10.1216/rmj-2013-43-1-361