论文标题
关于T-Adic Littlewood的猜想
On t-adic Littlewood conjecture for generalised Thue-Morse functions
论文作者
论文摘要
我们考虑一个由无限产品定义的laurent系列$ g_u（t）= \ prod_ {n = 0}^\ infty（1 + ut^{ - 2^n}）$，其中$ u \ in \ mathbb {f} $是一个参数和$ \ m athbb {f} $是一个字段。我们表明，对于所有$ u \ in \ mathbb {q} \ setMinus \ { - 1,0,1 \} $系列$ g_u（t）$不满足$ t $ adiC littlewood的猜想。另一方面，如果$ \ mathbb {f} $是有限的，则$ g_u（t）\ in \ mathbb {f}（（（t^{ - 1}））$是有理功能，或者它满足$ t $ - ad $ - ad $ - ad $ - ad $ - ad $ adic-adic littlewood猜想。
We consider a Laurent series defined by infinite products $g_u(t) = \prod_{n=0}^\infty (1 + ut^{-2^n})$, where $u\in \mathbb{F}$ is a parameter and $\mathbb{F}$ is a field. We show that for all $u\in\mathbb{Q}\setminus\{-1,0,1\}$ the series $g_u(t)$ does not satisfy the $t$-adic Littlewood conjecture. On the other hand, if $\mathbb{F}$ is finite then $g_u(t)\in \mathbb{F}((t^{-1}))$ is either a rational function or it satisfies the $t$-adic Littlewood conjecture.
