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On Quadratic Gauss Sums over Local Fields
1987The classical Gauss sum attached to the Legendre symbol \(\left( {\frac{.}{p}} \right)\)with an odd prime p is $$ {g_p} = \frac{1}{{\sqrt p }}\sum\limits_{\mathop {x\bmod p}\limits_{\left( {x,p} \right) = 1} } {\left( {\frac{x}{p}} \right){e^{2\pi ix/p}} = \frac{1}{{\sqrt p }}} \sum\limits_{x\bmod p} {{e^{2\pi i{x^2}/p}}} $$ which is equal to 1 ...
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Evaluation of a Class of Quadratic Gauss Sums by Sampling a Continuous Chirp Signal
Sampling Theory in Signal and Image Processing, 2016Summary: The calculation of discrete Fourier transform (DFT) of a periodic discrete-time chirp ends in the evaluation of a quadratic Gauss sum. The calculation of this sum has not been an easy problem in mathematics. It has taken years to be solved. In this work, by sampling a continuous chirp and relating the spectrum of the signal and the spectrum of
Dianat, Reza, Marvasti, Farokh
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Gauss Sums, Quadratic Reciprocity, and the Jacobi Symbol
2018Our first goal in this chapter is to present Gauss’s sixth proof of his Law of Quadratic Reciprocity. The presentation here follows [32, §3.3] fairly closely, except that our Gauss sums are over the complex numbers, as opposed to ibid. where Gauss sums are considered over a finite field. Later in the chapter we introduce the Jacobi symbol and study its
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A Hybrid Mean Value of L-Functions and General Quadratic Gauss Sums
2002The main purpose of this paper is using the estimates for character sums and the analytic method to study the 2k-th power mean of Dirichlet L-functions with the weight of general quadratic Gauss sums, and give an interesting asymptotic formula.
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Common Method Bias in Regression Models With Linear, Quadratic, and Interaction Effects
Organizational Research Methods, 2010Enno Siemsen +2 more
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OSQP: an operator splitting solver for quadratic programs
Mathematical Programming Computation, 2020Bartolomeo Stellato +2 more
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Discrete-Time Nonlinear Filtering Algorithms Using Gauss–Hermite Quadrature
Proceedings of the IEEE, 2007Robert J Elliott
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