Matches in SemOpenAlex for { <https://semopenalex.org/work/W4295332221> ?p ?o ?g. }
Showing items 1 to 55 of
55
with 100 items per page.
- W4295332221 abstract "Let ${mathbb F}_q$ be the finite field of $q$ elements, where $q=p^r$ is a power of the prime $p$, and $left(beta_1, beta_2, dots, beta_r right)$ be an ordered basis of ${mathbb F}_q$ over ${mathbb F}_p$. For $$xi=sum_{i=1}^rx_ibeta_i, quad quad x_iin{mathbb F}_p,$$ we define the Thue-Morse or sum-of-digits function $T(xi)$ on ${mathbb F}_q$ by [ T(xi)=sum_{i=1}^{r}x_i.%,quad xi=x_1beta_1+cdots +x_rbeta_rin {mathbb F}_q. ] For a given pattern length $s$ with $1le sle q$, a subset ${cal A}={alpha_1,ldots,alpha_s}subset {mathbb F}_q$, a polynomial $f(X)in{mathbb F}_q[X]$ of degree $d$ and a vector $underline{c}=(c_1,ldots,c_s)in{mathbb F}_p^s$ we put [ {cal T}(underline{c},{cal A},f)={xiin{mathbb F}_q : T(f(xi+alpha_i))=c_i,~i=1,ldots,s}. ] In this paper we will see that under some natural conditions, the size of~${cal T}(underline{c},{cal A},f)$ is asymptotically the same for all~$underline{c}$ and ${cal A}$ in both cases, $prightarrow infty$ and $rrightarrow infty$, respectively. More precisely, we have [ left||{cal T}(underline{c},{cal A},f)|-p^{r-s}right|le (d-1)q^{1/2}] under certain conditions on $d,q$ and $s$. For monomials of large degree we improve this bound as well as we find conditions on $d,q$ and $s$ for which this bound is not true. In particular, if $1le d<p$ we have the dichotomy that the bound is valid if $sle d$ and fails for some $underline{c}$ and ${cal A}$ if $sge d+1$. The case $s=1$ was studied before by Dartyge and S'arkozy." @default.
- W4295332221 created "2022-09-13" @default.
- W4295332221 creator A5013629904 @default.
- W4295332221 creator A5056642780 @default.
- W4295332221 date "2021-06-23" @default.
- W4295332221 modified "2023-10-14" @default.
- W4295332221 title "Normality of the Thue-Morse function for finite fields along polynomial values" @default.
- W4295332221 doi "https://doi.org/10.48550/arxiv.2106.12218" @default.
- W4295332221 hasPublicationYear "2021" @default.
- W4295332221 type Work @default.
- W4295332221 citedByCount "0" @default.
- W4295332221 crossrefType "posted-content" @default.
- W4295332221 hasAuthorship W4295332221A5013629904 @default.
- W4295332221 hasAuthorship W4295332221A5056642780 @default.
- W4295332221 hasBestOaLocation W42953322211 @default.
- W4295332221 hasConcept C11252640 @default.
- W4295332221 hasConcept C114614502 @default.
- W4295332221 hasConcept C121332964 @default.
- W4295332221 hasConcept C134306372 @default.
- W4295332221 hasConcept C14036430 @default.
- W4295332221 hasConcept C24890656 @default.
- W4295332221 hasConcept C2775997480 @default.
- W4295332221 hasConcept C33923547 @default.
- W4295332221 hasConcept C77926391 @default.
- W4295332221 hasConcept C78458016 @default.
- W4295332221 hasConcept C86803240 @default.
- W4295332221 hasConcept C90119067 @default.
- W4295332221 hasConceptScore W4295332221C11252640 @default.
- W4295332221 hasConceptScore W4295332221C114614502 @default.
- W4295332221 hasConceptScore W4295332221C121332964 @default.
- W4295332221 hasConceptScore W4295332221C134306372 @default.
- W4295332221 hasConceptScore W4295332221C14036430 @default.
- W4295332221 hasConceptScore W4295332221C24890656 @default.
- W4295332221 hasConceptScore W4295332221C2775997480 @default.
- W4295332221 hasConceptScore W4295332221C33923547 @default.
- W4295332221 hasConceptScore W4295332221C77926391 @default.
- W4295332221 hasConceptScore W4295332221C78458016 @default.
- W4295332221 hasConceptScore W4295332221C86803240 @default.
- W4295332221 hasConceptScore W4295332221C90119067 @default.
- W4295332221 hasLocation W42953322211 @default.
- W4295332221 hasOpenAccess W4295332221 @default.
- W4295332221 hasPrimaryLocation W42953322211 @default.
- W4295332221 hasRelatedWork W1557101139 @default.
- W4295332221 hasRelatedWork W1968915506 @default.
- W4295332221 hasRelatedWork W2042456698 @default.
- W4295332221 hasRelatedWork W2057954107 @default.
- W4295332221 hasRelatedWork W2156114253 @default.
- W4295332221 hasRelatedWork W2265965672 @default.
- W4295332221 hasRelatedWork W2970640972 @default.
- W4295332221 hasRelatedWork W2989875800 @default.
- W4295332221 hasRelatedWork W3089295049 @default.
- W4295332221 hasRelatedWork W3104137792 @default.
- W4295332221 isParatext "false" @default.
- W4295332221 isRetracted "false" @default.
- W4295332221 workType "article" @default.