Journal ArticleDOI
On the sum of digits of special sequences in finite fields
TLDR
The methods combine A. Weil bounds with character sums, Gaussian sums and exponential sums to provide sharp estimates for the number of elements of special sequences of Fq whose sum of digits is prescribed.Abstract:
In $$\mathbb {F}_q$$
, Dartyge and Sarkozy introduced the notion of digits and studied some properties of the sum of digits function. We will provide sharp estimates for the number of elements of special sequences of $$\mathbb {F}_q$$
whose sum of digits is prescribed. Such special sequences of particular interest include the set of n-th powers for each $$n\ge 1$$
and the set of elements of order d in $$\mathbb {F}_q^*$$
for each divisor d of $$q-1$$
. We provide an optimal estimate for the number of squares whose sum of digits is prescribed. Our methods combine A. Weil bounds with character sums, Gaussian sums and exponential sums.read more
Citations
More filters
Journal ArticleDOI
Arithmetic constraints of polynomial maps through discrete logarithms
TL;DR: In this paper, the distribution of the functions F i : y ↦ log θ P i ( y ) ( mod d i ), over the set F q ∖ ∪ i = 1 k { y ∈ F q | P i( y ) = 0 }.
Journal ArticleDOI
On the distribution of the Rudin-Shapiro function for finite fields
TL;DR: In this article, the Rudin-Shapiro function on the power of a prime over a polynomial integer over a fixed degree is defined and the number of solutions is asymptotically $p^{r-1}$ for any fixed degree.
Posted Content
Pseudorandom sequences derived from automatic sequences.
TL;DR: In this paper, the authors investigate properties of pseudorandomness and non-randomness of automatic sequences and their subsequences and present results on their behaviour under several measures of pseudoreandomness including linear complexity, correlation measure of order $k$, expansion complexity and normality.
Journal ArticleDOI
Normality of the Thue–Morse function for finite fields along polynomial values
TL;DR: In this paper , a finite field of q elements is defined, where q is a power of the prime p , and q is an ordered basis of $$\varvec{F}_q$$.
Posted Content
Character sums over affine spaces and applications
Lucas Reis,Eleonora Lima +1 more
TL;DR: This work provides a new bound on the sum $\sum_{a\in \mathcal A}\chi(a)$, where $\chi$ a multiplicative character of $\mathbb F_{q^n}$.
References
More filters
Book
An Introduction to the Theory of Numbers
TL;DR: The fifth edition of the introduction to the theory of numbers has been published by as discussed by the authors, and the main changes are in the notes at the end of each chapter, where the author seeks to provide up-to-date references for the reader who wishes to pursue a particular topic further and to present a reasonably accurate account of the present state of knowledge.
Book
Handbook of Finite Fields
Gary L. Mullen,Daniel Panario +1 more
TL;DR: The Handbook of Finite Fields describes various mathematical and practical applications of finite fields in combinatorics, algebraic coding theory, cryptographic systems, biology, quantum information theory, engineering, and other areas.
Journal ArticleDOI
Sur les nombres qui ont des propriétés additives et multiplicatives données
Journal ArticleDOI
Sur un problème de Gelfond: la somme des chiffres des nombres premiers
Christian Mauduit,Joël Rivat +1 more
TL;DR: In this paper, Gelfond et al. repondre to a question posed by Gentry in 1968, expressing equirepartie dans les progressions arithmetiques (except for certains cases degeneres bien connus).