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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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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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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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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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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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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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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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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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