{"title":"关于$$p$$ -一元局部泛函方程的说明","authors":"Luochen Zhao","doi":"10.1134/s2070046622030037","DOIUrl":null,"url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p> Given primes <span>\\(\\ell\\ne p\\)</span>, we record here a <span>\\(p\\)</span>-adic valued Fourier theory on a local field over <span>\\(\\mathbf{Q}_\\ell\\)</span>, which is developed under the perspective of group schemes. As an application, by substituting rigid analysis for complex analysis, it leads naturally to the <span>\\(p\\)</span>-adic local functional equation at <span>\\(\\ell\\)</span>, which strongly resembles the complex one in Tate’s thesis. </p>","PeriodicalId":44654,"journal":{"name":"P-Adic Numbers Ultrametric Analysis and Applications","volume":"17 1","pages":""},"PeriodicalIF":0.5000,"publicationDate":"2022-08-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Note on $$p$$ -Adic Local Functional Equation\",\"authors\":\"Luochen Zhao\",\"doi\":\"10.1134/s2070046622030037\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<h3 data-test=\\\"abstract-sub-heading\\\">Abstract</h3><p> Given primes <span>\\\\(\\\\ell\\\\ne p\\\\)</span>, we record here a <span>\\\\(p\\\\)</span>-adic valued Fourier theory on a local field over <span>\\\\(\\\\mathbf{Q}_\\\\ell\\\\)</span>, which is developed under the perspective of group schemes. As an application, by substituting rigid analysis for complex analysis, it leads naturally to the <span>\\\\(p\\\\)</span>-adic local functional equation at <span>\\\\(\\\\ell\\\\)</span>, which strongly resembles the complex one in Tate’s thesis. </p>\",\"PeriodicalId\":44654,\"journal\":{\"name\":\"P-Adic Numbers Ultrametric Analysis and Applications\",\"volume\":\"17 1\",\"pages\":\"\"},\"PeriodicalIF\":0.5000,\"publicationDate\":\"2022-08-05\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"P-Adic Numbers Ultrametric Analysis and Applications\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1134/s2070046622030037\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"MATHEMATICS, INTERDISCIPLINARY APPLICATIONS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"P-Adic Numbers Ultrametric Analysis and Applications","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1134/s2070046622030037","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MATHEMATICS, INTERDISCIPLINARY APPLICATIONS","Score":null,"Total":0}
Given primes \(\ell\ne p\), we record here a \(p\)-adic valued Fourier theory on a local field over \(\mathbf{Q}_\ell\), which is developed under the perspective of group schemes. As an application, by substituting rigid analysis for complex analysis, it leads naturally to the \(p\)-adic local functional equation at \(\ell\), which strongly resembles the complex one in Tate’s thesis.
期刊介绍:
This is a new international interdisciplinary journal which contains original articles, short communications, and reviews on progress in various areas of pure and applied mathematics related with p-adic, adelic and ultrametric methods, including: mathematical physics, quantum theory, string theory, cosmology, nanoscience, life sciences; mathematical analysis, number theory, algebraic geometry, non-Archimedean and non-commutative geometry, theory of finite fields and rings, representation theory, functional analysis and graph theory; classical and quantum information, computer science, cryptography, image analysis, cognitive models, neural networks and bioinformatics; complex systems, dynamical systems, stochastic processes, hierarchy structures, modeling, control theory, economics and sociology; mesoscopic and nano systems, disordered and chaotic systems, spin glasses, macromolecules, molecular dynamics, biopolymers, genomics and biology; and other related fields.