The level of distribution of the Thue--Morse sequence
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In: Compositio mathematica, Vol. 156, No. 12, 25.01.2021, p. 2560-2587.
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TY - JOUR
T1 - The level of distribution of the Thue--Morse sequence
AU - Spiegelhofer, Lukas
N1 - Publisher Copyright: © The Author(s) 2021.
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
KW - Thue-Morse sequence
KW - normal sequence
KW - Bombieri-Vinogradov theorem
KW - Elliott-Halberstam conjecture
KW - Piatetski-Shapiro sequence
KW - Gel'fond problem
KW - arithmetic progression
UR - http://www.scopus.com/inward/record.url?scp=85099960973&partnerID=8YFLogxK
U2 - 10.1112/S0010437X20007563
DO - 10.1112/S0010437X20007563
M3 - Article
VL - 156
SP - 2560
EP - 2587
JO - Compositio mathematica
JF - Compositio mathematica
SN - 0010-437x
IS - 12
ER -
