论文标题
非脾气多项式的Mahler度量的功能身份
A functional identity for Mahler measures of non-tempered polynomials
论文作者
论文摘要
我们建立了两个参数家族$ p_ {a，c}（x，y）= a（x+1/x）+y+y+1/y+c $的功能识别。我们的结果扩展了在Lalín，Zudilin和Samart的论文中证明的身份。作为副产品，我们获得$ m（p_ {a，c}）$的评估，对于$ a $ a $ a $ a $ a $ a $ c $的某些代数值的特殊值和$ l $ functions和booggarithms的评估。我们还为第一类和第三种椭圆形积分之间的一定身份的有效性提供了足够的条件，这意味着$ m（p_ {a，c}）$的几个身份。
We establish a functional identity for Mahler measures of the two-parametric family $P_{a,c}(x,y)=a(x+1/x)+y+1/y+c$. Our result extends an identity proven in a paper of Lalín, Zudilin and Samart. As a by-product, we obtain evaluations of $m(P_{a,c})$ for some algebraic values of $a$ and $c$ in terms of special values of $L$-functions and logarithms. We also give a sufficient condition for validity of a certain identity between the elliptic integrals of the first and the third kind, which implies several identities for $m(P_{a,c})$.
