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On Heilbronn's exponential sum [PDF]
The Quarterly Journal of Mathematics, 2012 In the paper we prove a new upper bound for Heilbronn's exponential sum and obtain some applications of our result to distribution of Fermat quotients.Comment: 10 ...
Shkredov, Ilya D.
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On the Application of a Hybrid Incomplete Exponential Sum to Aperiodic Hamming Correlation of Some Frequency-Hopping Sequences [PDF]
EntropyFrequency-hopping sequences are essential in frequency-hopping spread spectrum communication systems due to their strong anti-interference capabilities, low probability of interception, and high confidentiality.
Peihua Li, Hongyu Han
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On the exponential sum—product problem
Indagationes Mathematicae, 2008 Let \(p\) be a large prime and let \(g\) be an element of \(\mathbb F_p\) of a (large) multiplicative order \(T\). Given sets \(\mathcal A, \mathcal B \subset \mathbb Z_T^*\), consider the sets \[ \mathcal U = \{ g^{ab} : a \in \mathcal A, b \in \mathcal B \}, \quad \mathcal V = \{ g^{a} + g^{b} : a \in \mathcal A, b \in \mathcal B \}. \] In this paper,
Igor E Shparlinski
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Sum of Exponential Model for Fitting Data
Engineering Proceedings, 2023 As an approach to feature estimation, exponential fitting has attracted research interests in mathematical modeling. Semantic networks are used for numerous applications in computers, physics, and biology.
Ting-Cheng Chang, Min-Hao Wu, Ying Lin
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Goldbach partitions and norms of cusp forms
Journal of Numerical Analysis and Approximation Theory, 2019 An integral formula for the Goldbach partitions requires uniform convergence of a complex exponential sum. The dependence of the coefficients of the series is found to be bounded by that of cusp forms.
Simon Brian Davis
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Solution of differential equations using sum of exponential functions
Lietuvos Matematikos Rinkinys, 2004 In this paper algorithm for the expression power series to sum of exponential functions are presented. The results in case of operator solving method for differential equations are applied.
Liepa Bikulčienė, Zenonas Navickas
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, 2023 Using combinatorial techniques, we derive a recurrence identity that expresses an exponential power sum with negative powers in terms of another exponential power sum with positive powers. Consequently, we derive a formula for the power sum of the first $k$ natural numbers when the power is odd, which when used in combination with Faulhaber's formula ...
Thomas, Neha Elizabeth +1 more
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Decomposition of exponential sums based on subspace and its application in channel estimation
Dianxin kexue, 2023 The problem of the decomposition of an exponential sum sequence is a classical mathematical problem.Prony method and Prony-Kung method are the classical methods to solve this problem.The Prony-Kung method was analyzed in detail from the point of view of ...
Zhiwei WU +4 more
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Nonlinear Analysis, 2023 A new fractional difference with an exponential kernel function is proposed in this study. First, a difference operator is defined by the exponential function.
Guang Yang, Guo-Cheng Wu, Hui Fu
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Prony-Type Polynomials and Their Common Zeros
Frontiers in Applied Mathematics and Statistics, 2020 The problem of hidden periodicity of a bivariate exponential sum f(n)=∑j=1Najexp(-i〈ωj,n〉), where a1, …, aN ∈ ℂ\{0} and n ∈ ℤ2, is to recover frequency vectors ω1,…,ωN∈[0,2π) 2 using finitely many samples of f.
Jürgen Prestin, Hanna Veselovska
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