TY - JOUR

T1 - The level of distribution of the Thue--Morse sequence

AU - Spiegelhofer, Lukas

PY - 2021/1/25

Y1 - 2021/1/25

N2 - The level of distribution of a complex valued sequence b measuresthe 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 of a sequence satisfying a Bombieri--Vinogradov type theorem for each exponent θ<1.This result improves on the level of distribution 2/3 obtained by Müllner and the author.As an application of our method, we show that the subsequence of the Thue--Morse sequence indexed by [n^c], where 1simply normal. This result improves on the range 1

AB - The level of distribution of a complex valued sequence b measuresthe 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 of a sequence satisfying a Bombieri--Vinogradov type theorem for each exponent θ<1.This result improves on the level of distribution 2/3 obtained by Müllner and the author.As an application of our method, we show that the subsequence of the Thue--Morse sequence indexed by [n^c], where 1simply normal. This result improves on the range 1

KW - Thue--Morse Folge

KW - Arithmetische Progressionen

KW - Bombieri--Vinogradov Theorem

KW - Thue--Morse sequence

KW - level of distribution

KW - Bombieri--Vinogradov Theorem

U2 - 10.1112/S0010437X20007563

DO - 10.1112/S0010437X20007563

M3 - Article

VL - 156.2020

SP - 2560

EP - 2587

JO - Compositio mathematica

JF - Compositio mathematica

SN - 0010-437x

IS - 12

ER -