{"id":"https://openalex.org/W4365451299","doi":"https://doi.org/10.1007/s10998-023-00515-8","title":"On the size of a linear combination of two linear recurrence sequences over function fields","display_name":"On the size of a linear combination of two linear recurrence sequences over function fields","publication_year":2023,"publication_date":"2023-04-13","ids":{"openalex":"https://openalex.org/W4365451299","doi":"https://doi.org/10.1007/s10998-023-00515-8"},"language":"en","primary_location":{"id":"doi:10.1007/s10998-023-00515-8","is_oa":true,"landing_page_url":"http://dx.doi.org/10.1007/s10998-023-00515-8","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10998-023-00515-8.pdf","source":{"id":"https://openalex.org/S106707257","display_name":"Periodica Mathematica Hungarica","issn_l":"0031-5303","issn":["0031-5303","1588-2829"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Periodica Mathematica Hungarica","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://link.springer.com/content/pdf/10.1007/s10998-023-00515-8.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5042948256","display_name":"Sebastian Heintze","orcid":"https://orcid.org/0000-0002-6356-1986"},"institutions":[{"id":"https://openalex.org/I4092182","display_name":"Graz University of Technology","ror":"https://ror.org/00d7xrm67","country_code":"AT","type":"education","lineage":["https://openalex.org/I4092182"]}],"countries":["AT"],"is_corresponding":true,"raw_author_name":"Sebastian Heintze","raw_affiliation_strings":["Institute of Analysis and Number Theory, Graz University of Technology, Steyrergasse 30/II, A-8010, Graz, Austria"],"affiliations":[{"raw_affiliation_string":"Institute of Analysis and Number Theory, Graz University of Technology, Steyrergasse 30/II, A-8010, Graz, Austria","institution_ids":["https://openalex.org/I4092182"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5042948256"],"corresponding_institution_ids":["https://openalex.org/I4092182"],"apc_list":{"value":2290,"currency":"EUR","value_usd":2890},"apc_paid":{"value":2290,"currency":"EUR","value_usd":2890},"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.03289561,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"87","issue":"2","first_page":"283","last_page":"292"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11130","display_name":"Coding theory and cryptography","score":0.9927999973297119,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11130","display_name":"Coding theory and cryptography","score":0.9927999973297119,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.5655574202537537},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.33804085850715637},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.2874782383441925},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.2655293941497803}],"concepts":[{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.5655574202537537},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.33804085850715637},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.2874782383441925},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.2655293941497803}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/s10998-023-00515-8","is_oa":true,"landing_page_url":"http://dx.doi.org/10.1007/s10998-023-00515-8","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10998-023-00515-8.pdf","source":{"id":"https://openalex.org/S106707257","display_name":"Periodica Mathematica Hungarica","issn_l":"0031-5303","issn":["0031-5303","1588-2829"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Periodica Mathematica Hungarica","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.1007/s10998-023-00515-8","is_oa":true,"landing_page_url":"http://dx.doi.org/10.1007/s10998-023-00515-8","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10998-023-00515-8.pdf","source":{"id":"https://openalex.org/S106707257","display_name":"Periodica Mathematica Hungarica","issn_l":"0031-5303","issn":["0031-5303","1588-2829"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Periodica Mathematica Hungarica","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G4292615246","display_name":null,"funder_award_id":"I4406","funder_id":"https://openalex.org/F4320321181","funder_display_name":"Austrian Science Fund"}],"funders":[{"id":"https://openalex.org/F4320310430","display_name":"TU Graz, Internationale Beziehungen und Mobilit\u00e4tsprogramme","ror":"https://ror.org/00d7xrm67"},{"id":"https://openalex.org/F4320321181","display_name":"Austrian Science Fund","ror":"https://ror.org/013tf3c58"}],"has_content":{"grobid_xml":false,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4365451299.pdf"},"referenced_works_count":9,"referenced_works":["https://openalex.org/W1557415002","https://openalex.org/W1570844510","https://openalex.org/W2010931795","https://openalex.org/W2076027144","https://openalex.org/W2324974166","https://openalex.org/W2748040020","https://openalex.org/W3036392049","https://openalex.org/W3113470837","https://openalex.org/W4289527566"],"related_works":["https://openalex.org/W2051487156","https://openalex.org/W2073681303","https://openalex.org/W2544423928","https://openalex.org/W2052122378","https://openalex.org/W2053286651","https://openalex.org/W2181743346","https://openalex.org/W2187401768","https://openalex.org/W2181413294","https://openalex.org/W2989452537","https://openalex.org/W4313731559"],"abstract_inverted_index":{"Abstract":[0],"Let":[1],"$$":[2,4,13,15,39,49,51,73,75,84,86,153,160],"G_n":[3],"<mml:math":[5,16,42,52,76,87,109,161],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">":[6,17,43,53,77,88,110,162],"<mml:msub>":[7,18,78,119,124,134,171],"<mml:mi>G</mml:mi>":[8,120,135],"<mml:mi>n</mml:mi>":[9,121,136,166],"</mml:msub>":[10,21,81,122,127,137,174],"</mml:math>":[11,22,45,55,82,93,150,176],"and":[12,47,83],"H_m":[14],"<mml:mi>H</mml:mi>":[19,125],"<mml:mi>m</mml:mi>":[20,126,168],"be":[23,56],"two":[24],"non-degenerate":[25],"linear":[26],"recurrence":[27],"sequences":[28],"defined":[29],"over":[30,38],"a":[31,57],"function":[32],"field":[33],"F":[34,60],"in":[35],"one":[36],"variable":[37],"\\mathbb":[40],"{C}$$":[41],"<mml:mi>C</mml:mi>":[44,90,142],",":[46],"let":[48],"\\mu":[50,99,104],"<mml:mi>\u03bc</mml:mi>":[54,116,131],"valuation":[58],"on":[59],".":[61,177],"We":[62],"prove":[63],"that":[64,95],"under":[65],"suitable":[66],"conditions":[67],"there":[68],"are":[69],"effectively":[70],"computable":[71],"constants":[72],"c_1":[74,159],"<mml:mi>c</mml:mi>":[79,172],"<mml:mn>1</mml:mn>":[80,173],"C'":[85,107],"<mml:msup>":[89,141],"<mml:mo>\u2032</mml:mo>":[91,143],"</mml:msup>":[92,144],"such":[94],"the":[96],"bound":[97],"$$\\begin{aligned}":[98],"(G_n":[100],"-":[101],"H_m)":[102],"\\le":[103],"(G_n)":[105],"+":[106],"\\end{aligned}$$":[108],"<mml:mrow>":[111,115,117,132,163],"<mml:mtable>":[112],"<mml:mtr>":[113],"<mml:mtd>":[114],"<mml:mo>(</mml:mo>":[118,133],"<mml:mo>-</mml:mo>":[123],"<mml:mo>)</mml:mo>":[128,138],"</mml:mrow>":[129,139,145,149,175],"<mml:mo>\u2264</mml:mo>":[130],"<mml:mo>+</mml:mo>":[140],"</mml:mtd>":[146],"</mml:mtr>":[147],"</mml:mtable>":[148],"holds":[151],"for":[152],"\\max":[154],"\\left(":[155],"n,m":[156],"\\right)":[157],"&gt;":[158],"<mml:mo>max</mml:mo>":[164],"<mml:mfenced>":[165],"<mml:mo>,</mml:mo>":[167],"</mml:mfenced>":[169],"<mml:mo>&gt;</mml:mo>":[170]},"counts_by_year":[],"updated_date":"2026-04-10T15:06:20.359241","created_date":"2023-04-15T00:00:00"}
