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Quadratic Gaussian Sums

  • Bao Luong
Chapter
Part of the Applied and Numerical Harmonic Analysis book series (ANHA)

Abstract

Recall that the quadratic Gaussian sum of order n is the complexvalued function G n defined on the set of integers by the equation
$$G_n (x)\, = \,\frac{1}{{\sqrt n }}\,\sum\limits_{k \in Z_n } {e^{ - \frac{{2\Pi i}}{n}k^2 x} }.$$

If n is prime, then one may use the expression on the left of the equation in Theorem 1.2.3 as a definition for G n (x) (see page 71 of [7]).

Keywords

Prime Decomposition Finite Abelian Group Reduction Formula Previous Corollary Legendre Symbol 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Birkhäuser Boston 2009

Authors and Affiliations

  1. 1.Department of DefenseWashington

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