{"title":"随机对称p-adic矩阵等价类的分布","authors":"Valeriya Kovaleva","doi":"10.1112/mtk.12212","DOIUrl":null,"url":null,"abstract":"<p>We consider random symmetric matrices with independent entries distributed according to the Haar measure on <math>\n <semantics>\n <msub>\n <mi>Z</mi>\n <mi>p</mi>\n </msub>\n <annotation>$\\mathbb {Z}_p$</annotation>\n </semantics></math> for odd primes <i>p</i> and derive the distribution of their canonical form with respect to several equivalence relations. We give a few examples of applications including an alternative proof for the result of Bhargava, Cremona, Fisher, Jones and Keating on the probability that a random quadratic form over <math>\n <semantics>\n <msub>\n <mi>Z</mi>\n <mi>p</mi>\n </msub>\n <annotation>$\\mathbb {Z}_p$</annotation>\n </semantics></math> has a non-trivial zero.</p>","PeriodicalId":18463,"journal":{"name":"Mathematika","volume":null,"pages":null},"PeriodicalIF":0.8000,"publicationDate":"2023-06-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1112/mtk.12212","citationCount":"0","resultStr":"{\"title\":\"On the distribution of equivalence classes of random symmetric p-adic matrices\",\"authors\":\"Valeriya Kovaleva\",\"doi\":\"10.1112/mtk.12212\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>We consider random symmetric matrices with independent entries distributed according to the Haar measure on <math>\\n <semantics>\\n <msub>\\n <mi>Z</mi>\\n <mi>p</mi>\\n </msub>\\n <annotation>$\\\\mathbb {Z}_p$</annotation>\\n </semantics></math> for odd primes <i>p</i> and derive the distribution of their canonical form with respect to several equivalence relations. We give a few examples of applications including an alternative proof for the result of Bhargava, Cremona, Fisher, Jones and Keating on the probability that a random quadratic form over <math>\\n <semantics>\\n <msub>\\n <mi>Z</mi>\\n <mi>p</mi>\\n </msub>\\n <annotation>$\\\\mathbb {Z}_p$</annotation>\\n </semantics></math> has a non-trivial zero.</p>\",\"PeriodicalId\":18463,\"journal\":{\"name\":\"Mathematika\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.8000,\"publicationDate\":\"2023-06-19\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://onlinelibrary.wiley.com/doi/epdf/10.1112/mtk.12212\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Mathematika\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://onlinelibrary.wiley.com/doi/10.1112/mtk.12212\",\"RegionNum\":3,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Mathematika","FirstCategoryId":"100","ListUrlMain":"https://onlinelibrary.wiley.com/doi/10.1112/mtk.12212","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
On the distribution of equivalence classes of random symmetric p-adic matrices
We consider random symmetric matrices with independent entries distributed according to the Haar measure on for odd primes p and derive the distribution of their canonical form with respect to several equivalence relations. We give a few examples of applications including an alternative proof for the result of Bhargava, Cremona, Fisher, Jones and Keating on the probability that a random quadratic form over has a non-trivial zero.
期刊介绍：
Mathematika publishes both pure and applied mathematical articles and has done so continuously since its founding by Harold Davenport in the 1950s. The traditional emphasis has been towards the purer side of mathematics but applied mathematics and articles addressing both aspects are equally welcome. The journal is published by the London Mathematical Society, on behalf of its owner University College London, and will continue to publish research papers of the highest mathematical quality.
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