论 $$n$$ 有值动力学的增长函数

IF 0.6 4区数学 Q3 MATHEMATICS

Mathematical Notes Pub Date : 2024-07-05 DOI:10.1134/s0001434624030143

M. A. Chirkov

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引用次数: 0

摘要

摘要本文回答了 V. M. Buchstaber 提出的关于某些 $n$-valued 群的增长函数的问题。这个问题与特定的离散可积分系统密切相关。在本文中，我们找到了素 $n$ 情况下增长函数的具体公式。我们还证明了一般情况下增长函数的多项式渐近估计。最后，我们提出了关于增长函数的新猜想和问题。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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On the Growth Function of $$n$$ -Valued Dynamics

Abstract

This paper answers the question of V. M. Buchstaber on the growth function in case of certain $n$-valued group. This question is in close relation to specific discrete integrable systems. In the present paper, we find a specific formula for the growth function in the case of prime $n$. We also prove a polynomial asymptotic estimate of the growth function in the general case. At the end, we pose new conjectures and questions regarding growth functions.

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来源期刊

Mathematical Notes 数学-数学

CiteScore

0.90

自引率

16.70%

发文量

179

审稿时长

24 months

期刊介绍： Mathematical Notes is a journal that publishes research papers and review articles in modern algebra, geometry and number theory, functional analysis, logic, set and measure theory, topology, probability and stochastics, differential and noncommutative geometry, operator and group theory, asymptotic and approximation methods, mathematical finance, linear and nonlinear equations, ergodic and spectral theory, operator algebras, and other related theoretical fields. It also presents rigorous results in mathematical physics.