Results 231 to 240 of about 7,456 (263)
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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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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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1980
The Stickelberger theorem giving the factorization of Gauss sums, the Gross-Koblitz formula, and the Davenport-Hasse distribution relations will be combined to interpret Gauss sums as universal odd distributions (Yamamoto’s theorem).
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The Stickelberger theorem giving the factorization of Gauss sums, the Gross-Koblitz formula, and the Davenport-Hasse distribution relations will be combined to interpret Gauss sums as universal odd distributions (Yamamoto’s theorem).
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Maximally Equiangular Frames and Gauss Sums
Journal of Fourier Analysis and Applications, 2009zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Discrete-Time Nonlinear Filtering Algorithms Using Gauss–Hermite Quadrature
Proceedings of the IEEE, 2007Robert J Elliott
exaly