The level of distribution of the Thue–Morse sequence
The level of distribution of the Thue–Morse sequence
The level of distribution of a complex-valued sequence $b$ measures the quality of distribution of $b$ along sparse arithmetic progressions $nd+a$ . We prove that the Thue–Morse sequence has level of distribution $1$ , which is essentially best possible. More precisely, this sequence gives one of the first nontrivial examples …