Results 271 to 280 of about 884,151 (313)

On the gauss trigonometric sum

Mathematical Notes, 2000
The 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, 1997
It 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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Evaluation of the Hamming weights of a class of linear codes based on Gauss sums

Designs, Codes and Cryptography, 2015
Linear codes with a few weights have been widely investigated in recent years. In this paper, we mainly use Gauss sums to represent the Hamming weights of a class of q-ary linear codes under some certain conditions, where q is a power of a prime.
Ziling Heng, Q. Yue
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An explicit evaluation of $10^{\text{th}}$-power moment of quadratic Gauss sums and some applications

Functiones et Approximatio Commentarii Mathematici, 2022
Nilanjan Bag, Antonio Rojas-León, Zhang Wenpeng   +2 more
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ON THE CUBIC GAUSS SUM

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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Equidistribution of Gauss sums and Kloosterman sums

Mathematische Zeitschrift, 2004
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Fu, Lei, Liu, Chunlei
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Gauss and Jacobi Sums

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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Converse theorem of Gauss sums

, 2021
Chufeng Nien, Lei Zhang
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Sums Of Squares And Gauss Sums

1995
Abstract 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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Gauss Sums as Distributions

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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