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Gauss--Heilbronn Sums and Coverings of Deligne--Lusztig Type Curves [PDF]
Ito, Tetsushi +2 more
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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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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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Mathematika, 1976
Let N be a positive integer. We are concerned with the sumThus GN(N) is the ordinary Gauss sum. Previous methods of estimating such exponential sums have not brought to light the peculiar behaviour of GN(m) for m < N/2, namely that, for almost all values of m, GN(m) is in the vicinity of the point .
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Let N be a positive integer. We are concerned with the sumThus GN(N) is the ordinary Gauss sum. Previous methods of estimating such exponential sums have not brought to light the peculiar behaviour of GN(m) for m < N/2, namely that, for almost all values of m, GN(m) is in the vicinity of the point .
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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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On the gauss trigonometric sum
Mathematical Notes, 2000The author studies Gaussian sums of the form \(S(p,a,k)=\sum_{x=0}^{p-1}e^{2\pi iax^k/p}\), where \(a,k\) are positive integers, \(k\geq3, m=[(k-1)/2], a\not\equiv0\pmod p,\;p\equiv1\pmod k\). For \(p\equiv7\pmod{12}\) he proves a lower estimate of the form \(|S(p,a,6)|>(\sqrt3/2)\sqrt7\).
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Gauss Sums and Orthogonal Polynomials
International Journal of Modern Physics A, 1997It is shown that q-Hermite polynomials for q a root of unity are orthogonal on finite numbers of points of the real axes. The (complex) weight function coincides with a special type of the Gauss sums in number theory. The same Gauss sum plays the role of the weight function for the Stiltjes–Wigert and Rogers–Szegö polynomials leading to the ...
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