P-Adic Numbers Ultrametric Analysis and Applications最新文献

On Simultaneous Approximation of Algebraic Power Series over a Finite Field 论有限域上代数幂级数的同时逼近

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P-Adic Numbers Ultrametric Analysis and Applications Pub Date : 2024-07-30 DOI: 10.1134/s2070046624030063

Khalil Ayadi, Chiheb Ben Bechir, Samir Elkadri

引用次数: 0

$$H_A$$ -Weakly Periodic $$p$$ -Adic Generalized Gibbs Measures for the $$p$$ -Adic Ising Model on the Cayley Tree of Order Two 二阶 Cayley 树上 $$p$$ -Adic Ising 模型的弱周期 $$H_A$$ -p$$ -Adic 广义吉布斯度量

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P-Adic Numbers Ultrametric Analysis and Applications Pub Date : 2024-07-30 DOI: 10.1134/s2070046624030038

Muzaffar Rahmatullaev, Zulxumor Abdukaxorova

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$$p$$ -Adic Welch Bounds and $$p$$ -Adic Zauner Conjecture $$p$$ -阿迪克-韦尔奇边界和 $$p$$ -阿迪克-扎乌纳猜想

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P-Adic Numbers Ultrametric Analysis and Applications Pub Date : 2024-07-30 DOI: 10.1134/s207004662403004x

K. M. Krishna

{"title":"$$p$$ -Adic Welch Bounds and $$p$$ -Adic Zauner Conjecture","authors":"K. M. Krishna","doi":"10.1134/s207004662403004x","DOIUrl":"https://doi.org/10.1134/s207004662403004x","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3> Let (p) be a prime. For (din mathbb{N}), let (mathbb{Q}_p^d) be the standard (d)-dimensional p-adic Hilbert space. Let (m in mathbb{N}) and (text{Sym}^m(mathbb{Q}_p^d)) be the (p)-adic Hilbert space of symmetric m-tensors. We prove the following result. Let ({tau_j}_{j=1}^n) be a collection in (mathbb{Q}_p^d) satisfying (i) (langle tau_j, tau_jrangle =1) for all (1leq j leq n) and (ii) there exists (b in mathbb{Q}_p) satisfying (sum_{j=1}^{n}langle x, tau_jrangle tau_j =bx) for all ( x in mathbb{Q}^d_p.) Then $$begin{aligned} , max_{1leq j,k leq n, j neq k}{|n|, |langle tau_j, tau_krangle|^{2m} }geq frac{|n|^2}{left|{d+m-1 choose m}right| }. end{aligned}$$(0.1) We call Inequality (0.1) as the (p)-adic version of Welch bounds obtained by Welch [IEEE Transactions on Information Theory, 1974]. Inequality (0.1) differs from the non-Archimedean Welch bound obtained recently by M. Krishna as one can not derive one from another. We formulate (p)-adic Zauner conjecture. ","PeriodicalId":44654,"journal":{"name":"P-Adic Numbers Ultrametric Analysis and Applications","volume":"7 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2024-07-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141863710","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

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Finite Adelic Wavelet Bases and a Pseudodifferential Equation 有限阿德利小波基与伪微分方程

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P-Adic Numbers Ultrametric Analysis and Applications Pub Date : 2024-07-30 DOI: 10.1134/s2070046624030051

V. A. Aguilar-Arteaga, S. M. Delfín-Prieto, S. Estala-Arias

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Compactly Supported Distributions on $$p$$ -Adic Lie Groups 关于$$p$$-自洽李群的紧凑支持分布

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P-Adic Numbers Ultrametric Analysis and Applications Pub Date : 2024-07-30 DOI: 10.1134/s2070046624030014

Dubravka Ban, Jeremiah Roberts

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Rough Hardy-Littlewood Operators on $$p$$ -Adic Function Spaces with Variable Exponents 具有可变指数的$$p$$自变函数空间上的粗糙哈代-利特尔伍德算子

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P-Adic Numbers Ultrametric Analysis and Applications Pub Date : 2024-07-30 DOI: 10.1134/s2070046624030026

K. H. Dung, P. T. K. Thuy

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Approximation by Vallée-Poussin Type Means of Vilenkin-Fourier Series 维伦金-傅里叶级数的 Vallée-Poussin 型近似手段

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P-Adic Numbers Ultrametric Analysis and Applications Pub Date : 2024-07-30 DOI: 10.1134/s2070046624030075

S. S. Volosivets

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On the Theory of Relativistic Brownian Motion 论相对论布朗运动

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P-Adic Numbers Ultrametric Analysis and Applications Pub Date : 2024-05-06 DOI: 10.1134/s207004662402002x

E. A. Kurianovich, A. I. Mikhailov, I. V. Volovich

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The Collatz Conjecture & Non-Archimedean Spectral Theory - Part I - Arithmetic Dynamical Systems and Non-Archimedean Value Distribution Theory 科拉茨猜想与非阿基米德谱理论 - 第一部分 - 算术动态系统与非阿基米德值分布理论

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P-Adic Numbers Ultrametric Analysis and Applications Pub Date : 2024-05-06 DOI: 10.1134/s2070046624020055

Maxwell C. Siegel

{"title":"The Collatz Conjecture & Non-Archimedean Spectral Theory - Part I - Arithmetic Dynamical Systems and Non-Archimedean Value Distribution Theory","authors":"Maxwell C. Siegel","doi":"10.1134/s2070046624020055","DOIUrl":"https://doi.org/10.1134/s2070046624020055","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3> Let (q) be an odd prime, and let (T_{q}:mathbb{Z}rightarrowmathbb{Z}) be the Shortened (qx+1) map, defined by (T_{q}left(nright)=n/2) if (n) is even and (T_{q}left(nright)=left(qn+1right)/2) if (n) is odd. The study of the dynamics of these maps is infamous for its difficulty, with the characterization of the dynamics of (T_{3}) being an alternative formulation of the famous Collatz Conjecture. This series of papers presents a new paradigm for studying such arithmetic dynamical systems by way of a neglected area of ultrametric analysis which we have termed (left(p,qright))-adic analysis, the study of functions from the (p)-adics to the (q)-adics, where (p) and (q) are distinct primes. In this, the first paper, working with the (T_{q}) maps as a toy model for the more general theory, for each odd prime (q), we construct a function (chi_{q}:mathbb{Z}_{2}rightarrowmathbb{Z}_{q}) (the Numen of (T_{q})) and prove the Correspondence Principle (CP): (xinmathbb{Z}backslashleft{ 0right} ) is a periodic point of (T_{q}) if and only there is a (mathfrak{z}inmathbb{Z}_{2}backslashleft{ 0,1,2,ldotsright} ) so that (chi_{q}left(mathfrak{z}right)=x). Additionally, if (mathfrak{z}inmathbb{Z}_{2}backslashmathbb{Q}) makes (chi_{q}left(mathfrak{z}right)inmathbb{Z}), then the iterates of (chi_{q}left(mathfrak{z}right)) under (T_{q}) tend to (+infty) or (-infty). ","PeriodicalId":44654,"journal":{"name":"P-Adic Numbers Ultrametric Analysis and Applications","volume":"81 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2024-05-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140932394","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

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Group Structure of the $$p$$ -Adic Ball and Dynamical System of Isometry on a Sphere 球面上 $$p$$ 阿迪克球的群结构和等值动态系统

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P-Adic Numbers Ultrametric Analysis and Applications Pub Date : 2024-05-06 DOI: 10.1134/s2070046624020031

I. A. Sattarov

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