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Image Matching: Foundations, State of the Art, and Future Directions. [PDF]
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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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2021
We introduce Pell forms and show they lead us in a natural way to quadratic Gauss sums. We point out connections to the analytic class number formula and the modularity of elliptic curves.
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We introduce Pell forms and show they lead us in a natural way to quadratic Gauss sums. We point out connections to the analytic class number formula and the modularity of elliptic curves.
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1982
The method by which we proved the quadratic reciprocity in Chapter 5 is ingenious but is not easy to use in more general situations. We shall give a new proof in this chapter that is based on methods that can be used to prove higher reciprocity laws. In particular, we shall introduce the notion of a Gauss sum, which will play an important role in the ...
Kenneth Ireland, Michael Rosen
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The method by which we proved the quadratic reciprocity in Chapter 5 is ingenious but is not easy to use in more general situations. We shall give a new proof in this chapter that is based on methods that can be used to prove higher reciprocity laws. In particular, we shall introduce the notion of a Gauss sum, which will play an important role in the ...
Kenneth Ireland, Michael Rosen
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The American Mathematical Monthly, 2014
Let p be an odd prime and be a primitive pth-root of unity. For any integer a prime to p, let . a / denote the Legendre symbol, which is 1 if a is a square mod p, and is 1 otherwise. Using Euler's Criterion that a .p 1/=2 D. a / mod p, it follows that the Legendre symbol gives a homomorphism from the multiplicative group of nonzero elements F p of FpD ...
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Let p be an odd prime and be a primitive pth-root of unity. For any integer a prime to p, let . a / denote the Legendre symbol, which is 1 if a is a square mod p, and is 1 otherwise. Using Euler's Criterion that a .p 1/=2 D. a / mod p, it follows that the Legendre symbol gives a homomorphism from the multiplicative group of nonzero elements F p of FpD ...
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Lithuanian Mathematical Journal, 2017
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Lv, Xingxing, Zhang, Wenpeng
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zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Lv, Xingxing, Zhang, Wenpeng
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On some hybrid power moments of products of generalized quadratic Gauss sums and Kloosterman sums*
Lithuanian Mathematical Journal, 2018zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Djanković, Goran +3 more
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On the fourth power mean of the generalized quadratic Gauss sums
Acta Mathematica Sinica, English Series, 2017zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Zhang, Wen Peng, Lin, Xin
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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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