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A note on exponential sums [PDF]
Pacific Journal of Mathematics, 1969 The paper begins with a few applications of Rédei's theorem on sums of the form \( B=\sum_{s=1}^{p-1} c_{\delta} \zeta^{s} \) where \( c_{s}= \pm 1 \) and \( \zeta \) is a primitive \( p \)-th root of unity. (See this Zbl. 29, 109.) For instance it is proved that \( |B|^{2} \equiv 0(\bmod p) \) if and only if \( B \) is a Gauss sum, i. e.
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From Oscillatory Integrals and Sublevel Sets to Polynomial Congruences and Character Sums [PDF]
, 2010 We present a slight extension of a classical lemma of Hensel and give various applications to polynomial congruences and character sums; in particular, we give a new proof of a classical result of Hua on complete exponential sums.
Wright, James
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Sharp Estimates for Proximity of Geometric and Related Sums Distributions to Limit Laws
Mathematics, 2022 The convergence rate in the famous Rényi theorem is studied by means of the Stein method refinement. Namely, it is demonstrated that the new estimate of the convergence rate of the normalized geometric sums to exponential law involving the ideal ...
Alexander Bulinski, Nikolay Slepov
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A Hybrid Mean Value Involving the Two-Term Exponential Sums and Two-Term Character Sums
Journal of Applied Mathematics, 2014 The main purpose of this paper is using the properties of Gauss sums and the estimate for character sums to study the hybrid mean value problem involving the two-term exponential sums and two-term character sums and give an interesting asymptotic formula
Liu Miaohua, Li Xiaoxue
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Exponential sums with reducible polynomials
Discrete Analysis, 2019 Exponential sums with reducible polynomials, Discrete Analysis 2019:15, 31 pp. A sequence $(a_n)$ of real numbers in the interval $[0,1]$ is said to be _equidistributed_ if for every subinterval $[a,b]$ of $[0,1]$, the proportion of the $a_n$ that live
Cécile Dartyge, Greg Martin
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Decomposing Jacobians of Curves over Finite Fields in the Absence of Algebraic Structure [PDF]
, 2014 We consider the issue of when the L-polynomial of one curve over $\F_q$ divides the L-polynomial of another curve. We prove a theorem which shows that divisibility follows from a hypothesis that two curves have the same number of points over infinitely ...
Ahmadi, Omran +2 more
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On values of exponential sums [PDF]
Proceedings of the American Mathematical Society, 1975 An exponential sum is defined by \[ G ( F , φ , α ) = ∑ γ ϵ ( Z / q Z )
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Israel Journal of Mathematics, 2000 15 pages, to appear in Israel J ...
Adolphson, Alan, Sperber, Steven
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The hybrid mean value of Dedekind sums and two-term exponential sums
Open Mathematics, 2016 In this paper, we use the mean value theorem of Dirichlet L-functions, the properties of Gauss sums and Dedekind sums to study the hybrid mean value problem involving Dedekind sums and the two-term exponential sums, and give an interesting identity and ...
Leran Chang, Xiaoxue Li
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The hybrid power mean of the quartic Gauss sums and the two-term exponential sums
Advances in Difference Equations, 2018 In this paper, we use the analytic method and the properties of classical Gauss sums to study the computational problems of one kind hybrid power mean of quartic Gauss sums and two-term exponential sums, and give an interesting fourth-order linear ...
Xiaoxue Li
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