Quadratic Gaussian Sums

Part of the Applied and Numerical Harmonic Analysis book series (ANHA)


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]).


Prime Decomposition Finite Abelian Group Reduction Formula Previous Corollary Legendre Symbol 
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© Birkhäuser Boston 2009

Authors and Affiliations

  1. 1.Department of DefenseWashington

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