论文标题
多个变量中Mahler度量的限制
Limits of Mahler measures in multiple variables
论文作者
论文摘要
我们证明，通过单次替代从固定的月桂多项式P获得的劳伦多项式序列的某些序列产生了Mahler度量的序列，这些测量序列融合到Mahler量度。此外，我们为这种融合中的误差项提供了明确的上限，概括了迪米特罗夫和哈贝格的工作，并为2个可辩解的多项式家庭提供了全面的渐近扩展，其Mahler措施是由第三作者独立研究的。
We prove that certain sequences of Laurent polynomials, obtained from a fixed Laurent polynomial P by monomial substitutions, give rise to sequences of Mahler measures which converge to the Mahler measure of P. This generalizes previous work of Boyd and Lawton, who considered univariate monomial substitutions. We provide moreover an explicit upper bound for the error term in this convergence, generalizing work of Dimitrov and Habegger, and a full asymptotic expansion for a family of 2-variable polynomials, whose Mahler measures were studied independently by the third author.
