Additive patterns in a multiplicative group in a finite field

Choi, Geumlan; Zaharescu, Alexandru

doi:10.1007/s00229-003-0360-x

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Subsets Defined By Primitive Roots Polynomials and R-powers1

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2010

2023

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Cited by 2 publications

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“…First we will study a very general construction which combines primitive roots with polynomials and r-powers (see [3], [6], [7], and [14] for results on the distribution of r-powers).…”

Section: Subsets Defined By Primitive Roots Polynomials and R-powersmentioning

confidence: 99%

On the pseudo-randomness of subsets related to primitive roots

2010

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Many results have been proved on the distribution of the primitive roots. These results reflect certain random type properties of the set Gp of the primitive roots modulo p. This fact motivates the question that in what extent behaves Gp as a random subset of Zp? First a much more general form of this problem is studied by using the notion of pseudo-randomness of subsets of Zn which has been introduced and studied recently by Dartyge and Sárközy. This is followed by the study of the pseudo-randomness of a subset of Zp defined by index properties. In both cases it turns out that these subsets possess strong pseudo-random properties (the well-distribution measure and correlation measure of order k are small) but the pseudo-randomness is not perfect: there is a pseudo-random measure (the symmetry measure) which is large.

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“…First we will study a very general construction which combines primitive roots with polynomials and r-powers (see [3], [6], [7], and [14] for results on the distribution of r-powers).…”

Section: Subsets Defined By Primitive Roots Polynomials and R-powersmentioning

confidence: 99%