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1
Content available remote

A note on Waring's problem in finite fields

100%
Winterhof A.
Acta Arithmetica
|
2000-2001
|
tom 96
|
nr 4
365-368
2
Content available remote

On Waring's problem in finite fields

100%
Winterhof A.
Acta Arithmetica
|
1998-1999
|
tom 87
|
nr 2
171-177
3
Content available remote

Exact solutions to Waring's problem for finite fields

64%
Winterhof A., van de Woestijne C.
Acta Arithmetica
|
2010
|
tom 141
|
nr 2
171-190
4
Content available remote

Polynomial quotients: Interpolation, value sets and Waring's problem

64%
Chen Z., Winterhof A.
Acta Arithmetica
|
2015
|
tom 170
|
nr 2
121-134
EN
For an odd prime p and an integer w ≥ 1, polynomial quotients $q_{p,w}(u)$ are defined by $q_{p,w}(u) ≡ (u^w-u^{wp})/p mod p$ with $0 ≤ q_{p,w}(u) ≤ p-1$, u ≥ 0, which are generalizations of Fermat quotients $q_{p,p-1}(u)$. First, we estimate the number of elements $1 ≤ u < N ≤ p$ for which $f(u)≡ q_{p,w}(u) mod p$ for a given polynomial f(x) over the finite field $𝔽_p$. In particular, for the case f(x)=x we get bounds on the number of fixed points of polynomial quotients. Second, before we study the problem of estimating the smallest number (called the Waring number) of summands needed to express each element of $𝔽_p$ as a sum of values of polynomial quotients, we prove some lower bounds on the size of their value sets, and then we apply these lower bounds to prove some bounds on the Waring number using results about bounds on additive character sums and from additive number theory.
5
Content available remote

Incomplete character sums over finite fields and their application to the interpolation of the discrete logarithm by Boolean functions

64%
Lange T., Winterhof A.
Acta Arithmetica
|
2002
|
tom 101
|
nr 3
223-229
6
Content available remote

Incomplete exponential sums over finite fields and their applications to new inversive pseudorandom number generators

64%
Niederreiter H., Winterhof A.
Acta Arithmetica
|
2000
|
tom 93
|
nr 4
387-399
7
Content available remote

Multiplicative character sums for nonlinear recurring sequences

64%
Niederreiter H., Winterhof A.
Acta Arithmetica
|
2004
|
tom 111
|
nr 3
299-305
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