{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,2,21]],"date-time":"2025-02-21T07:50:48Z","timestamp":1740124248794,"version":"3.37.3"},"reference-count":9,"publisher":"Springer Science and Business Media LLC","issue":"2","license":[{"start":{"date-parts":[[2023,4,13]],"date-time":"2023-04-13T00:00:00Z","timestamp":1681344000000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2023,4,13]],"date-time":"2023-04-13T00:00:00Z","timestamp":1681344000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"funder":[{"DOI":"10.13039\/100008332","name":"Graz University of Technology","doi-asserted-by":"crossref","id":[{"id":"10.13039\/100008332","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Period Math Hung"],"published-print":{"date-parts":[[2023,12]]},"abstract":"Abstract<\/jats:title>Let $$ G_n $$<\/jats:tex-math>\n \n G<\/mml:mi>\n n<\/mml:mi>\n <\/mml:msub>\n <\/mml:math><\/jats:alternatives><\/jats:inline-formula> and $$ H_m $$<\/jats:tex-math>\n \n H<\/mml:mi>\n m<\/mml:mi>\n <\/mml:msub>\n <\/mml:math><\/jats:alternatives><\/jats:inline-formula> be two non-degenerate linear recurrence sequences defined over a function field F<\/jats:italic> in one variable over $$ \\mathbb {C}$$<\/jats:tex-math>\n C<\/mml:mi>\n <\/mml:math><\/jats:alternatives><\/jats:inline-formula>, and let $$ \\mu $$<\/jats:tex-math>\n \u03bc<\/mml:mi>\n <\/mml:math><\/jats:alternatives><\/jats:inline-formula> be a valuation on F<\/jats:italic>. We prove that under suitable conditions there are effectively computable constants $$ c_1 $$<\/jats:tex-math>\n \n c<\/mml:mi>\n 1<\/mml:mn>\n <\/mml:msub>\n <\/mml:math><\/jats:alternatives><\/jats:inline-formula> and $$ C' $$<\/jats:tex-math>\n \n C<\/mml:mi>\n \u2032<\/mml:mo>\n <\/mml:msup>\n <\/mml:math><\/jats:alternatives><\/jats:inline-formula> such that the bound $$\\begin{aligned} \\mu (G_n - H_m) \\le \\mu (G_n) + C' \\end{aligned}$$<\/jats:tex-math>\n \n \n \n \n \n \u03bc<\/mml:mi>\n \n (<\/mml:mo>\n \n G<\/mml:mi>\n n<\/mml:mi>\n <\/mml:msub>\n -<\/mml:mo>\n \n H<\/mml:mi>\n m<\/mml:mi>\n <\/mml:msub>\n )<\/mml:mo>\n <\/mml:mrow>\n \u2264<\/mml:mo>\n \u03bc<\/mml:mi>\n \n (<\/mml:mo>\n \n G<\/mml:mi>\n n<\/mml:mi>\n <\/mml:msub>\n )<\/mml:mo>\n <\/mml:mrow>\n +<\/mml:mo>\n \n C<\/mml:mi>\n \u2032<\/mml:mo>\n <\/mml:msup>\n <\/mml:mrow>\n <\/mml:mtd>\n <\/mml:mtr>\n <\/mml:mtable>\n <\/mml:mrow>\n <\/mml:math><\/jats:alternatives><\/jats:disp-formula>holds for $$ \\max \\left( n,m \\right) > c_1 $$<\/jats:tex-math>\n \n max<\/mml:mo>\n \n n<\/mml:mi>\n ,<\/mml:mo>\n m<\/mml:mi>\n <\/mml:mfenced>\n ><\/mml:mo>\n \n c<\/mml:mi>\n 1<\/mml:mn>\n <\/mml:msub>\n <\/mml:mrow>\n <\/mml:math><\/jats:alternatives><\/jats:inline-formula>.<\/jats:p>","DOI":"10.1007\/s10998-023-00515-8","type":"journal-article","created":{"date-parts":[[2023,4,13]],"date-time":"2023-04-13T13:17:03Z","timestamp":1681391823000},"page":"283-292","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["On the size of a linear combination of two linear recurrence sequences over function fields"],"prefix":"10.1007","volume":"87","author":[{"given":"Sebastian","family":"Heintze","sequence":"first","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2023,4,13]]},"reference":[{"issue":"3","key":"515_CR1","doi-asserted-by":"publisher","first-page":"427","DOI":"10.1017\/S0305004100066184","volume":"100","author":"WD Brownawell","year":"1986","unstructured":"W.D. Brownawell, D.W. Masser, Vanishing sums in function fields. Math. Proc. Camb. Phil. Soc. 100(3), 427\u2013434 (1986)","journal-title":"Math. Proc. Camb. Phil. Soc."},{"issue":"1","key":"515_CR2","doi-asserted-by":"publisher","first-page":"11","DOI":"10.1017\/S0004972720001094","volume":"104","author":"C Fuchs","year":"2021","unstructured":"C. Fuchs, S. Heintze, On the growth of linear recurrences in function fields. Bull. Austr. Math. Soc. 104(1), 11\u201320 (2021)","journal-title":"Bull. Austr. Math. Soc."},{"key":"515_CR3","doi-asserted-by":"publisher","first-page":"278","DOI":"10.1016\/j.jnt.2020.11.004","volume":"222","author":"C Fuchs","year":"2021","unstructured":"C. Fuchs, S. Heintze, A function field variant of Pillai\u2019s problem. J. Number Theory 222, 278\u2013292 (2021)","journal-title":"J. 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Math. 33(6), 1172\u20131188 (2022)","journal-title":"Indag. Math."},{"key":"515_CR7","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511566042","volume-title":"Exponential diophantine equations, Cambridge tracts in mathematics, 87","author":"TN Shorey","year":"1986","unstructured":"T.N. Shorey, R. Tijdeman, Exponential diophantine equations, Cambridge tracts in mathematics, 87 (Cambridge University Press, Cambridge, 1986)"},{"key":"515_CR8","volume-title":"Algebraic function fields and codes","author":"H Stichtenoth","year":"1993","unstructured":"H. Stichtenoth, Algebraic function fields and codes (Universitext, Springer, Berlin, 1993)"},{"issue":"1","key":"515_CR9","doi-asserted-by":"publisher","first-page":"127","DOI":"10.1007\/s00222-008-0136-8","volume":"174","author":"U Zannier","year":"2008","unstructured":"U. Zannier, On composite lacunary polynomials and the proof of a conjecture of Schinzel. Invent. Math. 174(1), 127\u2013138 (2008)","journal-title":"Invent. Math."}],"container-title":["Periodica Mathematica Hungarica"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10998-023-00515-8.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s10998-023-00515-8\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10998-023-00515-8.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,11,13]],"date-time":"2023-11-13T11:03:41Z","timestamp":1699873421000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s10998-023-00515-8"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,4,13]]},"references-count":9,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2023,12]]}},"alternative-id":["515"],"URL":"https:\/\/doi.org\/10.1007\/s10998-023-00515-8","relation":{},"ISSN":["0031-5303","1588-2829"],"issn-type":[{"type":"print","value":"0031-5303"},{"type":"electronic","value":"1588-2829"}],"subject":[],"published":{"date-parts":[[2023,4,13]]},"assertion":[{"value":"24 September 2022","order":1,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"13 April 2023","order":2,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}