• Title, Summary, Keyword: Gauss sum

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GAUSS SUMS FOR U(2n + 1,$q^2$)

  • Kim, Dae-San
    • Journal of the Korean Mathematical Society
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    • v.34 no.4
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    • pp.871-894
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    • 1997
  • For a lifted nontrivial additive character $\lambda'$ and a multiplicative character $\chi$ of the finite field with $q^2$ elements, the 'Gauss' sums $\Sigma\lambda'$(tr $\omega$) over $\omega$ $\in$ SU(2n + 1, $q^2$) and $\Sigma\chi$(det $\omega$)$\lambda'$(tr $\omega$) over $\omega$ $\in$ U(2n + 1, $q^2$) are considered. We show that the first sum is a polynomial in q with coefficients involving certain new exponential sums and that the second one is a polynomial in q with coefficients involving powers of the usual twisted Kloosterman sums and the average (over all multiplicative characters of order dividing q-1) of the usual Gauss sums. As a consequence we can determine certain 'generalized Kloosterman sum over nonsingular Hermitian matrices' which were previously determined by J. H. Hodges only in the case that one of the two arguments is zero.

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GAUSS SUMS OVER GALOIS RINGS OF CHARACTERISTIC 4

  • Oh, Yunchang;Oh, Heung-Joon
    • Korean Journal of Mathematics
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    • v.9 no.1
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    • pp.1-7
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    • 2001
  • In this paper, we define and study Gauss sums over Galois rings of characteristic 4. In particular, we give the absolute value of Gauss sum over Galois rings of characteristic 4.

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HYBRID MEAN VALUE OF GENERALIZED BERNOULLI NUMBERS, GENERAL KLOOSTERMAN SUMS AND GAUSS SUMS

  • Liu, Huaning;Zhang, Wenpeng
    • Journal of the Korean Mathematical Society
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    • v.44 no.1
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    • pp.11-24
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    • 2007
  • The main purpose of this paper is to use the properties of primitive characters, Gauss sums and Ramanujan's sum to study the hybrid mean value of generalized Bernoulli numbers, general Kloosterman sums and Gauss sums, and give two asymptotic formulae.

TRANSLATION AND HOMOTHETICAL SURFACES IN EUCLIDEAN SPACE WITH CONSTANT CURVATURE

  • Lopez, Rafael;Moruz, Marilena
    • Journal of the Korean Mathematical Society
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    • v.52 no.3
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    • pp.523-535
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    • 2015
  • We study surfaces in Euclidean space which are obtained as the sum of two curves or that are graphs of the product of two functions. We consider the problem of finding all these surfaces with constant Gauss curvature. We extend the results to non-degenerate surfaces in Lorentz-Minkowski space.

LEAST-SQUARES METHOD FOR THE BUBBLE STABILIZATION BY THE GAUSS-NEWTON METHOD

  • Kim, Seung Soo;Lee, Yong Hun;Oh, Eun Jung
    • Honam Mathematical Journal
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    • v.38 no.1
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    • pp.47-57
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    • 2016
  • In the discrete formulation of the bubble stabilized Legendre Galerkin methods, the system of equations includes the artificial viscosity term as the parameter. We investigate the estimation of this parameter to get the least-squares solution which minimizes the sum of the squares of errors at each node points. Some numerical results are reported.

ALTERNATIVE DERIVATIONS OF CERTAIN SUMMATION FORMULAS CONTIGUOUS TO DIXON'S SUMMATION THEOREM FOR A HYPERGEOMETRIC $_3F_2$ SERIES

  • Choi, June-Sang;Rathie Arjun K.;Malani Shaloo;Mathur Rachana
    • The Pure and Applied Mathematics
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    • v.13 no.4
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    • pp.255-259
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    • 2006
  • In 1994, Lavoie et al. have obtained twenty tree interesting results closely related to the classical Dixon's theorem on the sum of a $_3F_2$ by making a systematic use of some known relations among contiguous functions. We aim at showing that these results can be derived by using the same technique developed by Bailey with the help of Gauss's summation theorem and generalized Kummer's theorem obtained by Lavoie et al..

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FURTHER SUMMATION FORMULAS FOR THE APPELL'S FUNCTION $F_1$

  • CHOI JUNESANG;HARSH HARSHVARDHAN;RATHIE ARJUN K.
    • The Pure and Applied Mathematics
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    • v.12 no.3
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    • pp.223-228
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    • 2005
  • In 2001, Choi, Harsh & Rathie [Some summation formulas for the Appell's function $F_1$. East Asian Math. J. 17 (2001), 233-237] have obtained 11 results for the Appell's function $F_1$ with the help of Gauss's summation theorem and generalized Kummer's summation theorem. We aim at presenting 22 more results for $F_1$ with the help of the generalized Gauss's second summation theorem and generalized Bailey's theorem obtained by Lavoie, Grondin & Rathie [Generalizations of Whipple's theorem on the sum of a $_3F_2$. J. Comput. Appl. Math. 72 (1996), 293-300]. Two interesting (presumably) new special cases of our results for $F_1$ are also explicitly pointed out.

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GAUSS DISCREPANCY TYPE MEASURE OF DEGREE OF RESIDUALS FROM SYMMETRY FOR SQUARE CONTINGENCY TABLES

  • Tomizawa, Sadao;Murata, Mariko
    • Journal of the Korean Statistical Society
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    • v.21 no.1
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    • pp.59-69
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    • 1992
  • A measure is proposed to represent the degree of residuals from the symmetry model for square contingency tables with nominal categories. The measure is derivedby modifying the sum of squared singular values for a skew symmetric matrix of the residuals from the symmetry model. The proposed measure would be useful for comparing the degree of residuals from the symmetry model in several tables.

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