Matches in SemOpenAlex for { <https://semopenalex.org/work/W3132291063> ?p ?o ?g. }
Showing items 1 to 87 of
87
with 100 items per page.
- W3132291063 abstract "We prove effective joint equidistribution of several natural parameters associated to primitive vectors in $mathbb{Z}^{n}$, as the norm of these vectors tends to infinity. These parameters include the direction, the orthogonal lattice, and the length of the shortest solution to the associated $gcd$ equation. We show that the first two parameters equidistribute w.r.t. the Haar measure on the corresponding spaces, which are the unit sphere and the space of unimodular rank $n-1$ lattices in $mathbb{R}^{n}$ respectively. The main novelty is the equidistribution of the shortest solutions to the $gcd$ equations: we show that, when normalized by the covering radius of the orthogonal lattice, the lengths of these solutions equidistribute in the interval $left[0,1right]$ w.r.t. a measure that is Lebesgue only when $n=2$, and non-Lebesgue otherwise. These equidistribution results are deduced from effectively counting lattice points in domains which are defined w.r.t. a generalization of the Iwasawa decomposition in simple algebraic Lie groups, where we apply a method due to A. Gorodnik and A. Nevo." @default.
- W3132291063 created "2021-03-01" @default.
- W3132291063 creator A5009221747 @default.
- W3132291063 creator A5076154447 @default.
- W3132291063 date "2019-03-04" @default.
- W3132291063 modified "2023-09-27" @default.
- W3132291063 title "Equidistribution of primitive vectors, and the shortest solutions to their GCD equations" @default.
- W3132291063 cites W1605044767 @default.
- W3132291063 cites W1922550957 @default.
- W3132291063 cites W1931556517 @default.
- W3132291063 cites W1980672763 @default.
- W3132291063 cites W1999064304 @default.
- W3132291063 cites W2014802279 @default.
- W3132291063 cites W2024283190 @default.
- W3132291063 cites W2040131828 @default.
- W3132291063 cites W2070656973 @default.
- W3132291063 cites W2075275443 @default.
- W3132291063 cites W2084283992 @default.
- W3132291063 cites W2118549325 @default.
- W3132291063 cites W2120311787 @default.
- W3132291063 cites W2581927518 @default.
- W3132291063 cites W2962723677 @default.
- W3132291063 cites W2963971572 @default.
- W3132291063 cites W3100969409 @default.
- W3132291063 cites W3104453410 @default.
- W3132291063 cites W3106229159 @default.
- W3132291063 cites W3107453370 @default.
- W3132291063 cites W3122909321 @default.
- W3132291063 hasPublicationYear "2019" @default.
- W3132291063 type Work @default.
- W3132291063 sameAs 3132291063 @default.
- W3132291063 citedByCount "2" @default.
- W3132291063 countsByYear W31322910632020 @default.
- W3132291063 crossrefType "posted-content" @default.
- W3132291063 hasAuthorship W3132291063A5009221747 @default.
- W3132291063 hasAuthorship W3132291063A5076154447 @default.
- W3132291063 hasConcept C114614502 @default.
- W3132291063 hasConcept C121332964 @default.
- W3132291063 hasConcept C130805567 @default.
- W3132291063 hasConcept C134306372 @default.
- W3132291063 hasConcept C14158598 @default.
- W3132291063 hasConcept C191948623 @default.
- W3132291063 hasConcept C202444582 @default.
- W3132291063 hasConcept C24890656 @default.
- W3132291063 hasConcept C2777105136 @default.
- W3132291063 hasConcept C2781204021 @default.
- W3132291063 hasConcept C33923547 @default.
- W3132291063 hasConcept C9376300 @default.
- W3132291063 hasConceptScore W3132291063C114614502 @default.
- W3132291063 hasConceptScore W3132291063C121332964 @default.
- W3132291063 hasConceptScore W3132291063C130805567 @default.
- W3132291063 hasConceptScore W3132291063C134306372 @default.
- W3132291063 hasConceptScore W3132291063C14158598 @default.
- W3132291063 hasConceptScore W3132291063C191948623 @default.
- W3132291063 hasConceptScore W3132291063C202444582 @default.
- W3132291063 hasConceptScore W3132291063C24890656 @default.
- W3132291063 hasConceptScore W3132291063C2777105136 @default.
- W3132291063 hasConceptScore W3132291063C2781204021 @default.
- W3132291063 hasConceptScore W3132291063C33923547 @default.
- W3132291063 hasConceptScore W3132291063C9376300 @default.
- W3132291063 hasLocation W31322910631 @default.
- W3132291063 hasOpenAccess W3132291063 @default.
- W3132291063 hasPrimaryLocation W31322910631 @default.
- W3132291063 hasRelatedWork W1548129254 @default.
- W3132291063 hasRelatedWork W1747426553 @default.
- W3132291063 hasRelatedWork W2000969490 @default.
- W3132291063 hasRelatedWork W2038167022 @default.
- W3132291063 hasRelatedWork W2153145500 @default.
- W3132291063 hasRelatedWork W2238651674 @default.
- W3132291063 hasRelatedWork W2298969040 @default.
- W3132291063 hasRelatedWork W2316412685 @default.
- W3132291063 hasRelatedWork W2516913948 @default.
- W3132291063 hasRelatedWork W2735720405 @default.
- W3132291063 hasRelatedWork W2757627248 @default.
- W3132291063 hasRelatedWork W2912257391 @default.
- W3132291063 hasRelatedWork W2949825292 @default.
- W3132291063 hasRelatedWork W2951747939 @default.
- W3132291063 hasRelatedWork W2962707115 @default.
- W3132291063 hasRelatedWork W2962723677 @default.
- W3132291063 hasRelatedWork W2963381596 @default.
- W3132291063 hasRelatedWork W2963909868 @default.
- W3132291063 hasRelatedWork W3021636039 @default.
- W3132291063 hasRelatedWork W3082137030 @default.
- W3132291063 isParatext "false" @default.
- W3132291063 isRetracted "false" @default.
- W3132291063 magId "3132291063" @default.
- W3132291063 workType "article" @default.