TY - JOUR
T1 - Prime-representing functions and Hausdorff dimension
AU - Saito, K.
N1 - Publisher Copyright:
© 2021, Akadémiai Kiadó, Budapest, Hungary.
PY - 2021/10
Y1 - 2021/10
N2 - Let c≥ 2 be any fixed real number. Matomäki [4] inverstigated the set of A> 1 such that the integer part of Ack is a prime number for every k∈ N. She proved that the set is uncountable, nowhere dense, and has Lebesgue measure 0. In this article, we show that the set has Hausdorff dimension 1.
AB - Let c≥ 2 be any fixed real number. Matomäki [4] inverstigated the set of A> 1 such that the integer part of Ack is a prime number for every k∈ N. She proved that the set is uncountable, nowhere dense, and has Lebesgue measure 0. In this article, we show that the set has Hausdorff dimension 1.
KW - distribution of prime numbers
KW - Hausdorff dimension
KW - prime-representing function
UR - https://www.scopus.com/pages/publications/85114195626
U2 - 10.1007/s10474-021-01170-6
DO - 10.1007/s10474-021-01170-6
M3 - Article
AN - SCOPUS:85114195626
SN - 0236-5294
VL - 165
SP - 203
EP - 217
JO - Acta Mathematica Hungarica
JF - Acta Mathematica Hungarica
IS - 1
ER -