{"title":"局部p进微分方程","authors":"M. Put, L. Taelman","doi":"10.1063/1.2193131","DOIUrl":null,"url":null,"abstract":"This paper studies divergence in solutions of p-adic linear local differential equations. Such divergence is related to the notion of p-adic Liouville numbers. Also, the influence of the divergence on the differential Galois groups of such differential equations is explored. A complete result is given for second order equations and a conjecture for higher order equations is proposed.","PeriodicalId":210679,"journal":{"name":"Default journal","volume":"38 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2006-03-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"2","resultStr":"{\"title\":\"Local p-Adic Differential Equations\",\"authors\":\"M. Put, L. Taelman\",\"doi\":\"10.1063/1.2193131\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"This paper studies divergence in solutions of p-adic linear local differential equations. Such divergence is related to the notion of p-adic Liouville numbers. Also, the influence of the divergence on the differential Galois groups of such differential equations is explored. A complete result is given for second order equations and a conjecture for higher order equations is proposed.\",\"PeriodicalId\":210679,\"journal\":{\"name\":\"Default journal\",\"volume\":\"38 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2006-03-31\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"2\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Default journal\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1063/1.2193131\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Default journal","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1063/1.2193131","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
This paper studies divergence in solutions of p-adic linear local differential equations. Such divergence is related to the notion of p-adic Liouville numbers. Also, the influence of the divergence on the differential Galois groups of such differential equations is explored. A complete result is given for second order equations and a conjecture for higher order equations is proposed.
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