Results 141 to 150 of about 165,955 (179)
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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 Cubic Exponential Sums and Gauss Sums
Journal of Mathematical Sciences, 2018zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Exponential Sums over Finite Fields
Journal of Systems Science and Complexity, 2021zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Exponential Sums with a Difference
Proceedings of the London Mathematical Society, 1990This paper extends work on exponential sums by \textit{E. Bombieri} and \textit{H. Iwaniec} [Ann. Sc. Norm. Super. Pisa Cl. Sci., IV. Ser. 13, 449-472 (1986; Zbl 0615.10047)], \textit{H. Iwaniec} and \textit{C. J. Mozzochi} [J. Number Theory 29, No.1, 60-93 (1988; Zbl 0644.10031)] and \textit{M. N. Huxley} [Proc. Lond. Math. Soc., III. Ser.
Heath-Brown, D. R., Huxley, M. N.
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1996
Abstract We resume the treatment of the simple exponential sum in one variable. from Chapter 7, obtaining the results of Huxley (1993a), extended to short intervals and congruence families. We use the notation of Chapter 7, and assume all the restrictions made there on the parameters N (length of short sums) and R (expected size of the ...
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Abstract We resume the treatment of the simple exponential sum in one variable. from Chapter 7, obtaining the results of Huxley (1993a), extended to short intervals and congruence families. We use the notation of Chapter 7, and assume all the restrictions made there on the parameters N (length of short sums) and R (expected size of the ...
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1991
Let $$ f\left( \lambda \right) = {{\alpha }_{k}}{{\lambda }^{k}} + ... + {{\alpha }_{1}}\lambda $$ be ak-th degree polynomial with coefficients in K. Let a =(αk…,α1) be the fractional ideal generated by (αk…,α1). Suppose that aδ=g/q, where g;q are two relatively prime ideals, and $$ S(f(x),q) = \sum\limits_{\lambda (q)} {E(f(\lambda ))} , $$
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Let $$ f\left( \lambda \right) = {{\alpha }_{k}}{{\lambda }^{k}} + ... + {{\alpha }_{1}}\lambda $$ be ak-th degree polynomial with coefficients in K. Let a =(αk…,α1) be the fractional ideal generated by (αk…,α1). Suppose that aδ=g/q, where g;q are two relatively prime ideals, and $$ S(f(x),q) = \sum\limits_{\lambda (q)} {E(f(\lambda ))} , $$
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1992
The simplest example of Weyl’s sums is the sum of the first degree $$ S(P) = \sum\limits_{x = Q + 1}^{Q + P} {{e^{2\pi i\alpha x}}.} $$ .
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The simplest example of Weyl’s sums is the sum of the first degree $$ S(P) = \sum\limits_{x = Q + 1}^{Q + P} {{e^{2\pi i\alpha x}}.} $$ .
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A-to-Z Guide to Thermodynamics, Heat and Mass Transfer, and Fluids Engineering, 2006
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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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