Results 221 to 230 of about 102,666 (260)
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Journal of Mathematical Sciences, 2006
Let \(p> 2\) be a prime and \(k\geq 2\), \(n\geq 2\). This paper concerns the exponential sum \[ \sum\limits^{p^n}_{x=1} e^{2\pi i (ax^k + bx) p^{-n}} \] where \(a, b\) are integers. This sum occurs in studies of Waring's problem. The author proves for this sum the bound \[ p^{(1-V)/2} p^{n/2} (b, p^n)^{1/2}\quad\text{for}\quad n\equiv 1\pmod k \] and ...
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Let \(p> 2\) be a prime and \(k\geq 2\), \(n\geq 2\). This paper concerns the exponential sum \[ \sum\limits^{p^n}_{x=1} e^{2\pi i (ax^k + bx) p^{-n}} \] where \(a, b\) are integers. This sum occurs in studies of Waring's problem. The author proves for this sum the bound \[ p^{(1-V)/2} p^{n/2} (b, p^n)^{1/2}\quad\text{for}\quad n\equiv 1\pmod k \] and ...
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ON A CERTAIN GENERAL EXPONENTIAL SUM
International Journal of Number Theory, 2005In this paper we study the general exponential sum related to multiplicative functions f(n) with |f(n)| ≤ 1, namely we study the sum [Formula: see text] and obtain a non-trivial upper bound when α is a certain type of rational number.
Maier, H., Sankaranarayanan, A.
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Proceedings of the London Mathematical Society, 1936
Davenport, Harold, Heilbronn, H.
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Davenport, Harold, Heilbronn, H.
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Exponentially convergent lattice sums
Optics Letters, 2001For any oblique incidence and arbitrarily high order, lattice sums for one-dimensional gratings can be expressed in terms of exponentially convergent series. The scattering Green's function can be efficiently evaluated also in the grating plane. Numerical implementation of the method is 200 times faster than for the previous best result.
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On an estimate of a certain non-linear exponential sum
Indian Journal of Pure and Applied Mathematics, 2021C G Karthick Babu +2 more
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Distribution of Cubic Exponential Sums
Journal of Mathematical ScienceszbMATH Open Web Interface contents unavailable due to conflicting licenses.
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The Concentration of the Product of Exponentials Around the Exponential of the Sum
The American Mathematical Monthly, 2023Michael Anshelevich, Austin Pritchett
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Technical Note—On Matrix Exponential Differentiation with Application to Weighted Sum Distributions
Operations Research, 2022Milan Kumar Das +2 more
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The n-fold convolution of generalized exponential-sum distribution functions
Applied Mathematics and Computation, 2003Naiyang Ma
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