quadratic gauss sum

Quadratic Gauss sum

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In number theory, quadratic Gauss sums are certain finite sums of roots of unity. A quadratic Gauss sum can be interpreted as a linear combination of the ...

EVALUATION OF THE QUADRATIC GAUSS SUM

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As a consequence, we evaluate the quadratic Gauss sum and derive the law of quadratic reciprocity using only elementary methods. 1. Introduction.

The quadratic Gauss sum redux

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... Gauss's) is the quadratic Gauss sum, g = p−1. X a=1. ( a p. )ζa, and Gauss's calculation that g2 = (. −1 p. )p. (1). The purpose of this note is to present a ...

Gauss Sums

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is known as a Gauss sum ... p has an equal number of quadratic residues and quadratic non-residues. ... This completes the proof of the Gauss sum formula. Page 7 ...

Reference Request

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Let N≥2 be a natural number, then let χ:(Z/NZ)×→±1} be a quadratic character. Consider the Gauss sum τ(1,χ)=∑x∈(Z/NZ)×χ(x)e2πix/N.

(PDF) Note on the quadratic Gauss sums

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We study the relation between the Gauss and the quadratic Gauss sums. It is shown that the quadratic Gauss sums G(k;p) are equal to the Gauss ...

On some conjectures on generalized quadratic Gauss ...

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Abstract. The main purpose of this article is to study higher power mean values of generalized quadratic Gauss sums using estimates for character sums, analytic ...

How to prove a generalized Gauss sum formula

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The quadratic Gauss sum is given by G(s;k)=k−1∑x=0e(sx2k),. where e(α)=e2πıα, s is any integer coprime to p and k is a positive integer.

[ANT11] Quadratic Gauss sums

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