论文标题
广义thue-morse三角多项式的多重分析
Multifractal Analysis of generalized Thue-Morse trigonometric polynomials
论文作者
论文摘要
We consider the generalized Thue-Morse sequences $(t_n^{(c)})_{n\ge 0}$ ($c \in [0,1)$ being a parameter) defined by $t_n^{(c)} = e^{2πi c s_2(n)}$, where $s_2(n)$ is the sum of digits of the binary expansion of $n$.对于多项式，$σ_{n}^{（c）}（x）：= \ sum_ {n = 0}^{n-1} t_n^{（c）} e^{2πin x} $，我们在[18]中证明了统一的norm norm norm $ $ $ $ \ | = $ \ | f cundy ucry ucry ucry ust $ n^{γ（c）} $和最佳指数$γ（c）$是计算的。在本文中，我们研究了点的行为，并对极限$ \ lim_ {n \ to \ infty} n^{ - 1} \ log | = |σ_{2^n}^{（c）}（c）}（x）| $进行完整的多效分析。
We consider the generalized Thue-Morse sequences $(t_n^{(c)})_{n\ge 0}$ ($c \in [0,1)$ being a parameter) defined by $t_n^{(c)} = e^{2πi c s_2(n)}$, where $s_2(n)$ is the sum of digits of the binary expansion of $n$. For the polynomials $σ_{N}^{(c)} (x) := \sum_{n=0}^{N-1} t_n^{(c)} e^{2πi n x}$, we have proved in [18] that the uniform norm $\|σ_N^{(c)}\|_\infty$ behaves like $N^{γ(c)}$ and the best exponent $γ(c)$ is computed. In this paper, we study the pointwise behavior and give a complete multifractal analysis of the limit $\lim_{n\to\infty}n^{-1}\log |σ_{2^n}^{(c)}(x)|$.
