{"id":"https://openalex.org/W2059184876","doi":"https://doi.org/10.1090/s0025-5718-01-01353-9","title":"On the spatial distribution of solutions of decomposable form equations","display_name":"On the spatial distribution of solutions of decomposable form equations","publication_year":2001,"publication_date":"2001-08-03","ids":{"openalex":"https://openalex.org/W2059184876","doi":"https://doi.org/10.1090/s0025-5718-01-01353-9","mag":"2059184876"},"language":"en","primary_location":{"id":"doi:10.1090/s0025-5718-01-01353-9","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-01-01353-9","pdf_url":"https://www.ams.org/mcom/2002-71-238/S0025-5718-01-01353-9/S0025-5718-01-01353-9.pdf","source":{"id":"https://openalex.org/S102439543","display_name":"Mathematics of Computation","issn_l":"0025-5718","issn":["0025-5718","1088-6842"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Computation","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"bronze","oa_url":"https://www.ams.org/mcom/2002-71-238/S0025-5718-01-01353-9/S0025-5718-01-01353-9.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5084363747","display_name":"Graham Everest","orcid":null},"institutions":[{"id":"https://openalex.org/I1118541","display_name":"University of East Anglia","ror":"https://ror.org/026k5mg93","country_code":"GB","type":"education","lineage":["https://openalex.org/I1118541"]}],"countries":["GB"],"is_corresponding":true,"raw_author_name":"G. Everest","raw_affiliation_strings":["School of Mathematics, University of East Anglia, Norwich, Norfolk NR4 7TJ, United Kingdom","School of Mathematics, University of East Anglia, Norwich, Norfolk, NR4 7TJ, United Kingdom"],"affiliations":[{"raw_affiliation_string":"School of Mathematics, University of East Anglia, Norwich, Norfolk NR4 7TJ, United Kingdom","institution_ids":["https://openalex.org/I1118541"]},{"raw_affiliation_string":"School of Mathematics, University of East Anglia, Norwich, Norfolk, NR4 7TJ, United Kingdom","institution_ids":["https://openalex.org/I1118541"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5048968726","display_name":"Istv\u00e1n Ga\u00e1l","orcid":"https://orcid.org/0000-0002-8266-9570"},"institutions":[{"id":"https://openalex.org/I132735039","display_name":"University of Debrecen","ror":"https://ror.org/02xf66n48","country_code":"HU","type":"education","lineage":["https://openalex.org/I132735039"]}],"countries":["HU"],"is_corresponding":false,"raw_author_name":"I. Ga\u00e1l","raw_affiliation_strings":["Institute of Mathematics and Informatics, Lajos Kossuth University, H-4010 Debrecen, Pf 12, Hungary"],"affiliations":[{"raw_affiliation_string":"Institute of Mathematics and Informatics, Lajos Kossuth University, H-4010 Debrecen, Pf 12, Hungary","institution_ids":["https://openalex.org/I132735039"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5111781502","display_name":"K\u00e1lm\u00e1n Gy\u0151ry","orcid":"https://orcid.org/0000-0002-3133-3081"},"institutions":[{"id":"https://openalex.org/I132735039","display_name":"University of Debrecen","ror":"https://ror.org/02xf66n48","country_code":"HU","type":"education","lineage":["https://openalex.org/I132735039"]}],"countries":["HU"],"is_corresponding":false,"raw_author_name":"K. Gy\u00f6ry","raw_affiliation_strings":["Institute of Mathematics and Informatics, Lajos Kossuth University, H-4010 Debrecen, Pf 12, Hungary"],"affiliations":[{"raw_affiliation_string":"Institute of Mathematics and Informatics, Lajos Kossuth University, H-4010 Debrecen, Pf 12, Hungary","institution_ids":["https://openalex.org/I132735039"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5081018593","display_name":"Christian R\u00f6ttger","orcid":null},"institutions":[{"id":"https://openalex.org/I1118541","display_name":"University of East Anglia","ror":"https://ror.org/026k5mg93","country_code":"GB","type":"education","lineage":["https://openalex.org/I1118541"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"C. R\u00f6ttger","raw_affiliation_strings":["School of Mathematics, University of East Anglia, Norwich, Norfolk, NR4 7TJ, United Kingdom"],"affiliations":[{"raw_affiliation_string":"School of Mathematics, University of East Anglia, Norwich, Norfolk, NR4 7TJ, United Kingdom","institution_ids":["https://openalex.org/I1118541"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5084363747"],"corresponding_institution_ids":["https://openalex.org/I1118541"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":3,"citation_normalized_percentile":{"value":0.17924404,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":94,"max":96},"biblio":{"volume":"71","issue":"238","first_page":"633","last_page":"648"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10061","display_name":"Algebraic Geometry and Number Theory","score":0.9994000196456909,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10061","display_name":"Algebraic Geometry and Number Theory","score":0.9994000196456909,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11680","display_name":"Advanced Algebra and Geometry","score":0.9944000244140625,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12812","display_name":"Meromorphic and Entire Functions","score":0.9911999702453613,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8072834014892578},{"id":"https://openalex.org/keywords/unit-sphere","display_name":"Unit sphere","score":0.6767030954360962},{"id":"https://openalex.org/keywords/abelian-group","display_name":"Abelian group","score":0.5435386300086975},{"id":"https://openalex.org/keywords/maple","display_name":"Maple","score":0.5115528702735901},{"id":"https://openalex.org/keywords/integral-equation","display_name":"Integral equation","score":0.5022332668304443},{"id":"https://openalex.org/keywords/norm","display_name":"Norm (philosophy)","score":0.4299287796020508},{"id":"https://openalex.org/keywords/constellation","display_name":"Constellation","score":0.42717689275741577},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.41494864225387573},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.3631976842880249},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.33018049597740173},{"id":"https://openalex.org/keywords/law","display_name":"Law","score":0.0745968222618103}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8072834014892578},{"id":"https://openalex.org/C191948623","wikidata":"https://www.wikidata.org/wiki/Q1307800","display_name":"Unit sphere","level":2,"score":0.6767030954360962},{"id":"https://openalex.org/C136170076","wikidata":"https://www.wikidata.org/wiki/Q181296","display_name":"Abelian group","level":2,"score":0.5435386300086975},{"id":"https://openalex.org/C2780414537","wikidata":"https://www.wikidata.org/wiki/Q42292","display_name":"Maple","level":2,"score":0.5115528702735901},{"id":"https://openalex.org/C27016315","wikidata":"https://www.wikidata.org/wiki/Q580101","display_name":"Integral equation","level":2,"score":0.5022332668304443},{"id":"https://openalex.org/C191795146","wikidata":"https://www.wikidata.org/wiki/Q3878446","display_name":"Norm (philosophy)","level":2,"score":0.4299287796020508},{"id":"https://openalex.org/C70352696","wikidata":"https://www.wikidata.org/wiki/Q8928","display_name":"Constellation","level":2,"score":0.42717689275741577},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.41494864225387573},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.3631976842880249},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.33018049597740173},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.0745968222618103},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C59822182","wikidata":"https://www.wikidata.org/wiki/Q441","display_name":"Botany","level":1,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C1276947","wikidata":"https://www.wikidata.org/wiki/Q333","display_name":"Astronomy","level":1,"score":0.0},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.0}],"mesh":[],"locations_count":6,"locations":[{"id":"doi:10.1090/s0025-5718-01-01353-9","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-01-01353-9","pdf_url":"https://www.ams.org/mcom/2002-71-238/S0025-5718-01-01353-9/S0025-5718-01-01353-9.pdf","source":{"id":"https://openalex.org/S102439543","display_name":"Mathematics of Computation","issn_l":"0025-5718","issn":["0025-5718","1088-6842"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Computation","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.192.3145","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.192.3145","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.ams.org/journals/mcom/2002-71-238/S0025-5718-01-01353-9/S0025-5718-01-01353-9.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.43.9272","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.43.9272","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.mth.uea.ac.uk/~h090/up.ps","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.83.6359","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.83.6359","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.public.iastate.edu/~roettger/pub/up.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.97.4038","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.97.4038","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.ams.org/mcom/2002-71-238/S0025-5718-01-01353-9/S0025-5718-01-01353-9.pdf","raw_type":"text"},{"id":"pmh:oai:dea.lib.unideb.hu:2437/273955","is_oa":true,"landing_page_url":"http://ebib.lib.unideb.hu/ebib/?action=cclfind&resultview=long&ccltext=idno+bibEBI00025256","pdf_url":null,"source":{"id":"https://openalex.org/S4306402089","display_name":"University of Debrecen Electronic Archive (University of Debrecen)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I132735039","host_organization_name":"University of Debrecen","host_organization_lineage":["https://openalex.org/I132735039"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"idegen nyelv\u0171 foly\u00f3iratk\u00f6zlem\u00e9ny k\u00fclf\u00f6ldi lapban"}],"best_oa_location":{"id":"doi:10.1090/s0025-5718-01-01353-9","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-01-01353-9","pdf_url":"https://www.ams.org/mcom/2002-71-238/S0025-5718-01-01353-9/S0025-5718-01-01353-9.pdf","source":{"id":"https://openalex.org/S102439543","display_name":"Mathematics of Computation","issn_l":"0025-5718","issn":["0025-5718","1088-6842"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Computation","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320322192","display_name":"Magyar Tudom\u00e1nyos Akad\u00e9mia","ror":"https://ror.org/02ks8qq67"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2059184876.pdf","grobid_xml":"https://content.openalex.org/works/W2059184876.grobid-xml"},"referenced_works_count":12,"referenced_works":["https://openalex.org/W337056928","https://openalex.org/W1486926352","https://openalex.org/W1493951387","https://openalex.org/W1509169162","https://openalex.org/W1512531712","https://openalex.org/W1550664183","https://openalex.org/W1607458528","https://openalex.org/W2320497937","https://openalex.org/W2911614147","https://openalex.org/W2979889824","https://openalex.org/W4237170929","https://openalex.org/W4249713408"],"related_works":["https://openalex.org/W3008027610","https://openalex.org/W2619973341","https://openalex.org/W4300811723","https://openalex.org/W2210259036","https://openalex.org/W2019433297","https://openalex.org/W2970670716","https://openalex.org/W4249171332","https://openalex.org/W2522483390","https://openalex.org/W650945805","https://openalex.org/W2966474385"],"abstract_inverted_index":{"We":[0],"study":[1],"the":[2,7,18,34,39,49,68,77,93],"distribution":[3],"in":[4,38,85,108],"space":[5],"of":[6,20,33,61,79,95,97],"integral":[8,12],"solutions":[9,22,35,101],"to":[10,102,118],"an":[11],"decomposable":[13],"form":[14,104],"equation,":[15],"by":[16,89],"considering":[17],"images":[19],"these":[21,122],"under":[23],"central":[24],"projection":[25],"onto":[26],"a":[27,58,116],"unit":[28,52],"ball.":[29],"If":[30],"we":[31,42],"think":[32],"as":[36],"stars":[37],"night":[40],"sky,":[41],"ask":[43],"what":[44,129],"constellations":[45],"are":[46,55,64],"visible":[47],"from":[48],"earth":[50],"(the":[51],"ball).":[53],"Answers":[54],"given":[56],"for":[57],"large":[59],"class":[60],"examples":[62],"which":[63],"then":[65],"illustrated":[66],"using":[67],"software":[69],"packages":[70],"KANT":[71],"and":[72,82,106,128],"Maple.":[73],"These":[74],"pictures":[75],"highlight":[76],"accuracy":[78],"our":[80,90,98,113],"predictions":[81],"arouse":[83],"interest":[84],"cases":[86],"not":[87],"covered":[88],"results.":[91],"Within":[92],"range":[94],"applicability":[96],"results":[99],"lie":[100],"norm":[103],"equations":[105],"units":[107],"abelian":[109],"group":[110],"rings.":[111],"Thus":[112],"theory":[114],"has":[115],"lot":[117],"say":[119],"about":[120],"where":[121],"interesting":[123],"objects":[124],"can":[125],"be":[126],"found":[127],"they":[130],"look":[131],"like.":[132]},"counts_by_year":[{"year":2013,"cited_by_count":2}],"updated_date":"2026-04-21T06:05:55.347736","created_date":"2025-10-10T00:00:00"}
