{"title":"正交群上的Kloosterman和。","authors":"Catinca Mujdei","doi":"10.1007/s11139-025-01135-1","DOIUrl":null,"url":null,"abstract":"<p><p>We study Kloosterman sums on the orthogonal groups <math><mrow><mi>S</mi> <msub><mi>O</mi> <mrow><mn>3</mn> <mo>,</mo> <mn>3</mn></mrow> </msub> </mrow> </math> and <math><mrow><mi>S</mi> <msub><mi>O</mi> <mrow><mn>4</mn> <mo>,</mo> <mn>2</mn></mrow> </msub> </mrow> </math> , associated to short elements of their respective Weyl groups. An explicit description for these sums is obtained in terms of multi-dimensional exponential sums. These are bounded by a combination of methods from algebraic geometry and <i>p</i>-adic analysis.</p>","PeriodicalId":54511,"journal":{"name":"Ramanujan Journal","volume":"67 4","pages":"94"},"PeriodicalIF":0.6000,"publicationDate":"2025-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC12185604/pdf/","citationCount":"0","resultStr":"{\"title\":\"Kloosterman sums on orthogonal groups.\",\"authors\":\"Catinca Mujdei\",\"doi\":\"10.1007/s11139-025-01135-1\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p><p>We study Kloosterman sums on the orthogonal groups <math><mrow><mi>S</mi> <msub><mi>O</mi> <mrow><mn>3</mn> <mo>,</mo> <mn>3</mn></mrow> </msub> </mrow> </math> and <math><mrow><mi>S</mi> <msub><mi>O</mi> <mrow><mn>4</mn> <mo>,</mo> <mn>2</mn></mrow> </msub> </mrow> </math> , associated to short elements of their respective Weyl groups. An explicit description for these sums is obtained in terms of multi-dimensional exponential sums. These are bounded by a combination of methods from algebraic geometry and <i>p</i>-adic analysis.</p>\",\"PeriodicalId\":54511,\"journal\":{\"name\":\"Ramanujan Journal\",\"volume\":\"67 4\",\"pages\":\"94\"},\"PeriodicalIF\":0.6000,\"publicationDate\":\"2025-01-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC12185604/pdf/\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Ramanujan Journal\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1007/s11139-025-01135-1\",\"RegionNum\":3,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"2025/6/23 0:00:00\",\"PubModel\":\"Epub\",\"JCR\":\"Q3\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Ramanujan Journal","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1007/s11139-025-01135-1","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"2025/6/23 0:00:00","PubModel":"Epub","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}
We study Kloosterman sums on the orthogonal groups and , associated to short elements of their respective Weyl groups. An explicit description for these sums is obtained in terms of multi-dimensional exponential sums. These are bounded by a combination of methods from algebraic geometry and p-adic analysis.
期刊介绍:
The Ramanujan Journal publishes original papers of the highest quality in all areas of mathematics influenced by Srinivasa Ramanujan. His remarkable discoveries have made a great impact on several branches of mathematics, revealing deep and fundamental connections.
The following prioritized listing of topics of interest to the journal is not intended to be exclusive but to demonstrate the editorial policy of attracting papers which represent a broad range of interest:
Hyper-geometric and basic hyper-geometric series (q-series) * Partitions, compositions and combinatory analysis * Circle method and asymptotic formulae * Mock theta functions * Elliptic and theta functions * Modular forms and automorphic functions * Special functions and definite integrals * Continued fractions * Diophantine analysis including irrationality and transcendence * Number theory * Fourier analysis with applications to number theory * Connections between Lie algebras and q-series.