Results 241 to 250 of about 40,388 (276)
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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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Mathematics of the USSR-Izvestiya, 1967
This article refutes the Kummer conjecture on the behavior of the argument of the cubic Gauss sum. It is proved that the prime numbers are uniformly distributed over the Kummer classes.
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This article refutes the Kummer conjecture on the behavior of the argument of the cubic Gauss sum. It is proved that the prime numbers are uniformly distributed over the Kummer classes.
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Equidistribution of Gauss sums and Kloosterman sums
Mathematische Zeitschrift, 2004zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Fu, Lei, Liu, Chunlei
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1982
In Chapter 6 we introduced the notion of a quadratic Gauss sum. In this chapter a more general notion of Gauss sum will be introduced. These sums have many applications. They will be used in Chapter 9 as a tool in the proofs of the laws of cubic and biquadratic reciprocity.
Kenneth Ireland, Michael Rosen
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In Chapter 6 we introduced the notion of a quadratic Gauss sum. In this chapter a more general notion of Gauss sum will be introduced. These sums have many applications. They will be used in Chapter 9 as a tool in the proofs of the laws of cubic and biquadratic reciprocity.
Kenneth Ireland, Michael Rosen
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Sums Of Squares And Gauss Sums
1995Abstract The concepts introduced so far form the basis for the major topics to be discussed in this chapter, they are Gauss sums and, to begin with, the representation of integers as sums of squares. Consider the proposition: if p is a prime and p = 1 (mod 4), then the Diophantine equation has an integer solution. This result.
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