Results 211 to 220 of about 87,373 (257)
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Estimates on polynomial exponential sums
Israel Journal of Mathematics, 2010Let \(f(x)=a_1x^{k_1}+\cdots+a_rx^{k_r}\in \mathbb{Z}[x]\) be a polynomial of degree \(d\), and let \(q\) be a positive integer. Assume \((a_1,\cdots,a_r,q)=1\), and define \(e_q(x)=e^{2\pi i \frac{x}{q}}\). This paper estimates exponential sums of the form \[ \sum_{1\leq x< q;~(x,q)=1}e_q(f(x)) \quad \text{and}\quad \sum_{1\leq x\leq q}e_q(f(x ...
J. Bourgain
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Estimates on exponential sums related to the Diffie–Hellman Distributions
GAFA Geometric And Functional Analysis, 2005This important paper investigates the structure of sets in \( \mathbb F_p \) and \( \mathbb F_p \times \mathbb F_p \) with small product set, where ``small'' is meant in the not too restrictive sense \(| H \cdot H| < | H| ^{1+\tau }\) with a suitably small \(\tau \).
J. Bourgain
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On Hua's estimates for exponential sums
Mathematika, 1987Let f(x)\(\in {\mathbb{Z}}[X]\), \(e_ q(t)=\exp (2\pi i/q)\) and \(S(q,f)=\sum _{0\leq ...
J. Chalk
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On the estimates of double exponential sums
Acta Arithmetica, 2007 Hong-Quan Liu
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On the Problem of Parameter Estimation in Exponential Sums
Constructive Approximation, 2011zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Filbir, F., Mhaskar, H. N., Prestin, J.
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Quality and Reliability Engineering International, 2020
AbstractAs a useful tool in statistical process control (SPC), the exponential control chart is more and more popular for monitoring high‐quality processes. Considering both known and estimated parameter cases, the one‐sided exponential cumulative sum (CUSUM) charts are studied in this paper through a Markov chain approach. Because the shape of the run
YuLong Qiao +3 more
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AbstractAs a useful tool in statistical process control (SPC), the exponential control chart is more and more popular for monitoring high‐quality processes. Considering both known and estimated parameter cases, the one‐sided exponential cumulative sum (CUSUM) charts are studied in this paper through a Markov chain approach. Because the shape of the run
YuLong Qiao +3 more
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Parameter estimation of monomial-exponential sums in one and two variables
Applied Mathematics and Computation, 2015zbMATH Open Web Interface contents unavailable due to conflicting licenses.
FERMO, LUISA +2 more
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On a variant of sum-product estimates and explicit exponential sum bounds in prime fields
Mathematical Proceedings of the Cambridge Philosophical Society, 2009AbstractLet Fp be the field of a prime order p and F*p be its multiplicative subgroup. In this paper we obtain a variant of sum-product estimates which in particular implies the bound for any subset A ⊂ Fp with 1 < |A| < p12/23. Then we apply our estimate to obtain explicit bounds for some exponential sums in Fp.
Bourgain, J., Garaev, M. Z.
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Estimates of hybrid exponential sums on quasiprojective varieties over finite fields
Mathematika, 1996Recently, \textit{E. Bombieri} and \textit{S. Sperber} [Acta Arith. 69, 329-358 (1995; Zbl 0826.11040)] have jointly created a new construction for estimating exponential sums on quasiprojective varieties over finite fields. In this paper we apply their construction to estimate hybrid exponential sums on quasiprojective varieties over finite fields. In
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Exponential Sums over Finite Fields
Journal of Systems Science and Complexity, 2021D. Wan
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