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数学与物理学

一个二元多项式的Mahler测度

  • 张安豪 ,
  • 唐国平
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  • 中国科学院大学数学科学学院, 北京 100049

收稿日期: 2022-04-25

  修回日期: 2022-06-08

  网络出版日期: 2022-05-26

基金资助

国家自然科学基金(11771422)资助

Mahler measure of a two-variable polynomial

  • ZHANG Anhao ,
  • TANG Guoping
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  • School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing 100049, China

Received date: 2022-04-25

  Revised date: 2022-06-08

  Online published: 2022-05-26

摘要

将一个二元多项式P(x,y)=(x2+1)y2+2(x2+x)y+x(x2+1)的Mahler测度表达成一些Bloch-Wigner双对数函数的线性和,进而得到其与χ-3L函数特殊值的有理倍数关系:m(P(x,y))=5/2L'(χ-3,-1)。

本文引用格式

张安豪 , 唐国平 . 一个二元多项式的Mahler测度[J]. 中国科学院大学学报, 2024 , 41(2) : 145 -150 . DOI: 10.7523/j.ucas.2022.060

Abstract

In this paper, we express the Mahler measure of a two-variable polynomial P(x,y)=(x2+1)y2+2(x2+x)y+x(x2+1) as a linear sum of some Bloch-Wigner Dilogarithm functions. and prove that the Mahler measure of P(x,y) is rationally proportional to L'(χ-3,-1):m(P(x,y))=5/2L'(χ-3,-1).

参考文献

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