Results 231 to 240 of about 4,354 (265)

On the distribution of cubic exponential sums

Forum Mathematicum, 2014
Using the theory of metaplectic forms, we study the asymptotic behavior of cubic exponential sums over the ring of Eisenstein integers. In the first part of the paper, some non-trivial estimates on average over arithmetic progressions are obtained.
Louvel, Benoit
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An Application of Exponential Sum Estimates

Acta Mathematica Sinica, English Series, 2004
Let \(p\) be an odd prime, \(\delta\) a fixed real with \(0 < \delta < 2\), and \(k, l\) fixed positive integers. Let \(N_{k, l}(p, \delta)\) denote the number of solutions of the inequality \[ \left| \left\{ a^k/p \right\} + \left\{ b^k/p \right\} - \left\{ \bar a^l/p \right\} - \left\{ \bar b^l/p \right\} \right| < \delta \] in \(a, b \in \mathbb F_p^
Yi, Yuan, Zhang, Wenpeng
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The Estimation of Complete Exponential Sums

Canadian Mathematical Bulletin, 1985
AbstractThis paper proves a conjecture of Loxton and Smith about the size of the exponential sum S(f;q) formed by summing exp (2πif(x)/q) over x mod q, where f is a polynomial of degree n with integer coefficients. It is shown that |S(f;q)| ≤ Cfdn(q)qe/(e+1), where e is the maximum of the orders of the complex zeros of f'.
Loxton, J. H., Vaughan, R. C.
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Improvements of 𝑝-adic estimates of exponential sums

Proceedings of the American Mathematical Society, 2022
Let n , r n, r and f f be positive integers. Let p p be a prime number and ψ \psi be an arbitrary fixed nontrivial additive character of the finite field F q \mathbb F_q with q =
Feng, Yulu, Hong, Shaofang
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Exponential estimates for the maximum of partial sums. I

Acta Mathematica Hungarica, 1979
F Mòricz, Mòricz F
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On the Problem of Parameter Estimation in Exponential Sums

Constructive Approximation, 2011
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Filbir, F., Mhaskar, H. N., Prestin, J.
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An Estimate of a Special Exponential Sum

Mathematische Nachrichten, 1986
The exponential sums \(\sum^{n}_{k=1}k^{2\pi ir}\), \(\sum^{\infty}_{k=1}k^{2\pi ir} e^{-k^ 2/n}\), and \(\sum^{n}_{k=1}k^{2\pi ir-1}\) are considered. These are closely related to Riemann's zeta-function (though the zeta-function is not mentioned in the paper), and the main results of the paper are either well-known from the theory of the zeta ...
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Estimates for exponential sums. Applications

Journal of Mathematical Sciences, 2012
We obtain estimates of exponential (in particular, trigonometric) sums in terms of rational functions. Examples of sharp inequalities are given. These inequalities are used for estimating solutions to linear homogeneous differential equations with constant coefficients.
V. I. Danchenko, A. E. Dodonov
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An estimate of theL 1-norm of an exponential sum

Mathematical Notes, 1996
The following theorem is proved. Suppose that \(A\geq 1/2\), \(10\) the inequality \[ \int_0^1 \Biggl| \sum_{n=1}^N \alpha_n \exp(2\pi ixf(n)) \Biggr| dx\geq \exp(2^{-15} A^{-2} (\log N)^{3-2\beta}) \] is valid. This improves an estimate of S. V. Bochkarev. The proof uses an estimate of a trigonometric sum due to O. V. Popov.
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Quadrature sums and Lagrange interpolation for general exponential weights

Journal of Computational and Applied Mathematics, 2003
We obtain forward and converse quadrature sum estimates associated with zeros of orthogonal polynomials for general exponential weights. These are then applied to establish mean convergence of Lagrange interpolation at zeros of these orthogonal ...
D S Lubinsky
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