{"doi":"10.5802/jtnb.819","publication":"Journal de Theorie des Nombres des Bordeaux","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","quality_controlled":"1","title":"Weak multipliers for generalized van der Corput sequences","issue":"3","article_type":"original","oa":1,"publication_identifier":{"eissn":["2118-8572"],"issn":["1246-7405"]},"language":[{"iso":"eng"}],"_id":"2904","scopus_import":"1","intvolume":"        24","file_date_updated":"2020-07-14T12:45:52Z","file":[{"file_name":"JTNB_2012__24_3_729_0.pdf","file_id":"7819","date_created":"2020-05-11T12:40:39Z","creator":"dernst","relation":"main_file","checksum":"6954bfe9d7f4119fbdda7a11cf0f5c67","content_type":"application/pdf","file_size":819275,"date_updated":"2020-07-14T12:45:52Z","access_level":"open_access"}],"publisher":"Université de Bordeaux","oa_version":"Published Version","day":"01","volume":24,"date_updated":"2023-10-18T07:53:47Z","ddc":["510"],"publication_status":"published","month":"01","page":"729 - 749","abstract":[{"text":"Generalized van der Corput sequences are onedimensional, infinite sequences in the unit interval. They are generated from permutations in integer base b and are the building blocks of the multi-dimensional Halton sequences. Motivated by recent progress of Atanassov on the uniform distribution behavior of Halton sequences, we study, among others, permutations of the form P(i) = ai (mod b) for coprime integers a and b. We show that multipliers a that either divide b - 1 or b + 1 generate van der Corput sequences with weak distribution properties. We give explicit lower bounds for the asymptotic distribution behavior of these sequences and relate them to sequences generated from the identity permutation in smaller bases, which are, due to Faure, the weakest distributed generalized van der Corput sequences.","lang":"eng"},{"lang":"fre","text":"Les suites de Van der Corput généralisées sont dessuites unidimensionnelles et infinies dans l’intervalle de l’unité.Elles sont générées par permutations des entiers de la basebetsont les éléments constitutifs des suites multi-dimensionnelles deHalton. Suites aux progrès récents d’Atanassov concernant le com-portement de distribution uniforme des suites de Halton nous nousintéressons aux permutations de la formuleP(i)  =ai(modb)pour les entiers premiers entre euxaetb. Dans cet article nousidentifions des multiplicateursagénérant des suites de Van derCorput ayant une mauvaise distribution. Nous donnons les bornesinférieures explicites pour cette distribution asymptotique asso-ciée à ces suites et relions ces dernières aux suites générées parpermutation d’identité, qui sont, selon Faure, les moins bien dis-tribuées des suites généralisées de Van der Corput dans une basedonnée."}],"date_published":"2012-01-01T00:00:00Z","has_accepted_license":"1","article_processing_charge":"No","status":"public","department":[{"_id":"HeEd"}],"author":[{"first_name":"Florian","last_name":"Pausinger","orcid":"0000-0002-8379-3768","full_name":"Pausinger, Florian","id":"2A77D7A2-F248-11E8-B48F-1D18A9856A87"}],"type":"journal_article","citation":{"ista":"Pausinger F. 2012. Weak multipliers for generalized van der Corput sequences. Journal de Theorie des Nombres des Bordeaux. 24(3), 729–749.","chicago":"Pausinger, Florian. “Weak Multipliers for Generalized van Der Corput Sequences.” <i>Journal de Theorie Des Nombres Des Bordeaux</i>. Université de Bordeaux, 2012. <a href=\"https://doi.org/10.5802/jtnb.819\">https://doi.org/10.5802/jtnb.819</a>.","apa":"Pausinger, F. (2012). Weak multipliers for generalized van der Corput sequences. <i>Journal de Theorie Des Nombres Des Bordeaux</i>. Université de Bordeaux. <a href=\"https://doi.org/10.5802/jtnb.819\">https://doi.org/10.5802/jtnb.819</a>","short":"F. Pausinger, Journal de Theorie Des Nombres Des Bordeaux 24 (2012) 729–749.","ama":"Pausinger F. Weak multipliers for generalized van der Corput sequences. <i>Journal de Theorie des Nombres des Bordeaux</i>. 2012;24(3):729-749. doi:<a href=\"https://doi.org/10.5802/jtnb.819\">10.5802/jtnb.819</a>","ieee":"F. Pausinger, “Weak multipliers for generalized van der Corput sequences,” <i>Journal de Theorie des Nombres des Bordeaux</i>, vol. 24, no. 3. Université de Bordeaux, pp. 729–749, 2012.","mla":"Pausinger, Florian. “Weak Multipliers for Generalized van Der Corput Sequences.” <i>Journal de Theorie Des Nombres Des Bordeaux</i>, vol. 24, no. 3, Université de Bordeaux, 2012, pp. 729–49, doi:<a href=\"https://doi.org/10.5802/jtnb.819\">10.5802/jtnb.819</a>."},"year":"2012","publist_id":"3843","date_created":"2018-12-11T12:00:15Z"}