Exponential Sums
نویسنده
چکیده
where we in introduce the standard notation e(x) = exp(2πix). Question 1.1. What is the magnitude of | ∑ x∈S e(x)|? By the trivial bound, we find that | ∑ x∈S e(x)| ≤ N , with equality whenever the terms are all equal. One can of course make the sum much smaller–simply sum the Nth roots of unity. In between these two extremes–completely in phase and maximally out of phase–we should consider what we expect for a generic or random sum. Example 1.1. Let xi be uniform independent variables on [0, 1]. Then
منابع مشابه
A Relation between Fourier Coefficients of Holomorphic Cusp Forms and Exponential Sums
We consider certain specific exponential sums related to holomorphic cusp forms, give a reformulation for the Lehmer conjecture and prove that certain exponential sums of Fourier coefficients of holomorphic cusp forms contain information on other similar non-overlapping exponential sums. Also, we prove an Omega result for short sums of Fourier coefficients.
متن کاملExponential Sums, Gauss Sums and Cyclic Codes
The dissertation consists of three articles in which the evaluation of certain exponential sums and Gauss sums and bounds for the absolute values of exponential sums are considered. The summary part of the thesis provides interpretations in terms of coding theory for the results obtained in the articles.
متن کاملT-adic Exponential Sums over Finite Fields
T -adic exponential sums associated to a Laurent polynomial f are introduced. They interpolate all classical p-power order exponential sums associated to f . The Hodge bound for the Newton polygon of L-functions of T -adic exponential sums is established. This bound enables us to determine, for all m, the Newton polygons of Lfunctions of p-power order exponential sums associated to an f which i...
متن کاملA Survey on Pure and Mixed Exponential Sums modulo Prime Powers
where p is a prime power, epm(·) is the additive character epm(x) = e m and χ is a multiplicative character (mod p). The goals of this paper are threefold; first, to point out the similarity between exponential sums over finite fields and exponential sums over residue class rings (mod p) with m ≥ 2; second, to show how mixed exponential sums can be reduced to pure exponential sums when m ≥ 2 an...
متن کاملA Hybrid Mean Value Involving Dedekind Sums and the General Exponential Sums
The main purpose of this paper is using the analytic method, A. Weil's classical work for the upper bound estimate of the general exponential sums, and the properties of Gauss sums to study the hybrid mean value problem involving Dedekind sums and the general exponential sums and give a sharp asymptotic formula for it.
متن کاملExponential sums, Gauss sums and irreducible cyclic codes
In this paper we shall develope a recursive method for computing exponential sums and Gauss sums in so called index 2 case. The method allows us to generalize previous results obtained by Baumert, Mykkeltveit and van der Vlugt.
متن کامل