The joint distribution of q-additive functions

Drmota, Michael

doi:10.4064/aa100-1-2

Cited by 19 publications

(16 citation statements)

References 19 publications

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“…where ϑ is defined by (15). The same estimate holds for I f (A, Tr F q t |L (Ker(l))) with m replaced with dim K Tr F q t |L (Ker(l)).…”

Section: Values Of Polynomials In Subspacesmentioning

confidence: 63%

Polynomial values in affine subspaces of finite fields

Ostafe

2019

JAMA

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In this paper we introduce a new approach and obtain new results for the problem of studying polynomial images of affine subspaces of finite fields. We improve and generalise several previous known results, and also extend the range of such results to polynomials of degrees higher than the characteristic of the field. Such results have a wide scope of applications similar to those associated with their counterparts studying consecutive intervals over prime fields instead of affine subspaces. Here we give only two immediate consequences: to a bound on the size of the intersection of orbits of polynomial dynamical systems with affine subspaces and to the Waring problem in affine subspaces. These results are based on estimates for a certain new type of exponential sums.

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“…where ϑ is defined by (15). The same estimate holds for I f (A, Tr F q t |L (Ker(l))) with m replaced with dim K Tr F q t |L (Ker(l)).…”

Section: Values Of Polynomials In Subspacesmentioning

confidence: 63%

Polynomial values in affine subspaces of finite fields

Ostafe

2019

JAMA

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“…For example, the sum-of-digits function is a q-additive function. The distribution behaviour of q-additive functions has been discussed by several authors (starting most probably with M. Mend6s France [18] and H. Delange [3], see also Coquet [2], Dumont and Thomas [10,11~,Manstavicius [16], and [6] for a list of further references).…”

Section: Introductionmentioning

confidence: 99%

The Zeckendorf expansion of polynomial sequences

Drmota¹,

Steiner²

2002

Journal De Théorie Des Nombres De Bordeaux

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“…g-additive functions have been extensively discussed in the literature, in particular their asymptotic distribution, see [1,3,4,5,6,7,8,9,11,12,14,15]. We cite three of these results (in a slightly modified form).…”

Section: Introductionmentioning

confidence: 99%

“…Theorem C. (Drmota [6]) Suppose that g 1 ≥ 2 and g 2 ≥ 2 are coprime integers and that f 1 and f 2 are completely g 1 -resp. g 2 -additive functions.…”

Section: Introductionmentioning

confidence: 99%