The quadratic Gauss sum

AbstractWe have seen, in the previous works [5], [6], that the argument of a certain product is closely connected to that of the cubic Gauss sum. Here the absolute value of the product will be investigated.

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Gauss and Eisenstein Sums of Order Twelve

Canadian Mathematical Bulletin ◽

10.4153/cmb-2003-036-9 ◽

2003 ◽

Vol 46 (3) ◽

pp. 344-355 ◽

Cited By ~ 1

Author(s):

S. Gurak

Keyword(s):

Positive Integer ◽

Finite Field ◽

Gauss Sum ◽

Trace Map ◽

Complete Determination ◽

Eisenstein Sums

AbstractLet q = pr with p an odd prime, and Fq denote the finite field of q elements. Let Tr : Fq → Fp be the usual trace map and set ζp = exp(2πi/p). For any positive integer e, define the (modified) Gauss sum gr(e) byRecently, Evans gave an elegant determination of g1(12) in terms of g1(3), g1(4) and g1(6) which resolved a sign ambiguity present in a previous evaluation. Here I generalize Evans' result to give a complete determination of the sum gr(12).

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On the 2k-th Power Mean of Inversion of L-functions with the Weight of the Gauss Sum

Acta Mathematica Sinica English Series ◽

10.1007/s10114-003-0285-z ◽

2004 ◽

Vol 20 (1) ◽

pp. 175-180 ◽

Cited By ~ 5

Author(s):

Yuan Yi ◽

Wen Peng Zhang

Keyword(s):

Gauss Sum ◽

Power Mean

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A Gauss sum estimate in arbitrary finite fields

Comptes Rendus Mathematique ◽

10.1016/j.crma.2006.01.022 ◽

2006 ◽

Vol 342 (9) ◽

pp. 643-646 ◽

Cited By ~ 17

Author(s):

Jean Bourgain ◽

Mei-Chu Chang

Keyword(s):

Finite Fields ◽

Gauss Sum

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On the mean value of the mixed exponential sums with Dirichlet characters and general gauss sum

Czechoslovak Mathematical Journal ◽

10.1007/s10587-013-0030-4 ◽

2013 ◽

Vol 63 (2) ◽

pp. 461-473

Author(s):

Yongguang Du ◽

Huaning Liu

Keyword(s):

Exponential Sums ◽

Mean Value ◽

Gauss Sum ◽

Dirichlet Characters ◽

The Mean

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Gauss Optics and Gauss Sum on an Optical Phenomena

Foundations of Physics ◽

10.1007/s10701-008-9233-1 ◽

2008 ◽

Vol 38 (8) ◽

pp. 758-777 ◽

Cited By ~ 1

Author(s):

Shigeki Matsutani

Keyword(s):

Gauss Sum ◽

Optical Phenomena

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An evaluation of mathematical functions to fit infrared band envelopes

Canadian Journal of Chemistry ◽

10.1139/v67-381 ◽

1967 ◽

Vol 45 (20) ◽

pp. 2347-2352 ◽

Cited By ~ 58

Author(s):

J. Pitha ◽

R. Norman Jones

Keyword(s):

Infrared Absorption ◽

Condensed Phase ◽

Gauss Sum ◽

Infrared Band ◽

Absorption Bands ◽

Mathematical Functions ◽

Analytical Functions ◽

Fitting Procedures ◽

Phase Systems ◽

Infrared Absorption Bands

Simulated infrared absorption bands of condensed phase systems have been fitted with simple analytical functions by least-squares procedures. The bands were of Cauchy (Lorentz) contour and were modified to conform with the finite spectral slit distortion of the spectrophotometer. Cauchy, Cauchy–Gauss product, and Cauchy–Gauss sum functions were used in the fitting procedures using transmittance ordinates. The fits achieved were compared and the dependence of the optimized indices on the band distortion and data range were analyzed. Some preference for the Cauchy–Gauss sum function is indicated.

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