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New Identities Dealing with Gauss Sums
Symmetry, 2020 In this article, we used the elementary methods and the properties of the classical Gauss sums to study the problem of calculating some Gauss sums. In particular, we obtain some interesting calculating formulas for the Gauss sums corresponding to the ...
Abdul Samad, Wenpeng Zhang
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Incomplete higher-order Gauss sums [PDF]
Journal of Mathematical Analysis and Applications, 2003 We consider the classical incomplete higher-order Gauss sums Sm(B)=∑j=0Bexp(2πijm/N),0 ...
Bennet Yee +5 more
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Moments of Generalized Quadratic Gauss Sums Weighted by L-Functions [PDF]
Journal of Number Theory, 2002 The main purpose of this paper is using estimates for character sums and analytic methods to study the second, fourth, and sixth order moments of generalized quadratic Gauss sums weighted by L-functions.
Wenpeng Zhang
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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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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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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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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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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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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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An algebraic interpretation of the gauss sums
International Journal of Computer Mathematics, 2001Let be a finite arithmetic sequence in C with elements the values of a Dirichlet character Ξ mod n. If Xis the circulant n × n matrix with elements Ξ(i) then the eigenvalues of X are the Gauss sums that correspond to Ξ. Moreover, if Ξ=Ξ1 is the principal Dirichlet character mod n, then the eigenvalues of X are the Ramanujan sums C n(K).
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