Symbole de Newton. Symbole de Jacobi-Carlitz |
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| Institution: | 1. School of Computer Science and Technology, Dongguan University of Technology, Dongguan 523808, PR China;2. Department of Mathematics, Southern University of Science and Technology, Shenzhen 518055, PR China;1. Texas State University, United States of America;2. Yale University, United States of America;1. American Institute of Mathematics, 600 East Brokaw Road, San Jose, CA 95112-1006, United States;2. Bucknell University, Department of Physics and Astronomy, Lewisburg, PA 17837, United States;3. Chalmers University of Technology and University of Gothenburg, Department of Mathematics, Gothenburg, Sweden |
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| Abstract: | First of all we define the “Newton symbol” of two polynomials with coefficients in a commutative ring. The “Artinian symbol” of two polynomials of F2t] is then defined by analogy with the quadratic residue symbol. We prove that the Artinian symbol satisfies an “Euler's criterion”, and we define a “Jacobi-Carlitz symbol” in terms of the Newton symbol. |
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