Premium
REMARQUES SUR UNE SOMME LIÉE À LA FONCTION DE MÖBIUS
Author(s) -
Bretèche Régis de la,
Dress François,
Tenenbaum Gérald
Publication year - 2020
Publication title -
mathematika
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.955
H-Index - 29
eISSN - 2041-7942
pISSN - 0025-5793
DOI - 10.1112/mtk.12021
Subject(s) - mathematics , combinatorics , integer (computer science) , constant (computer programming) , computer science , programming language
For integer n ⩾ 1 and real z ⩾ 1 , define M ( n , z ) : = ∑ d | n , d ⩽ z μ ( d ) , where μ denotes the Möbius function. Put L ( y ) : = exp { ( log y ) 3 / 5 / ( log 2 y ) 1 / 5 }( y ⩾ 3 ) . We show that, for a suitable, explicit constant L > 0 and some constant c > 0 , we have S ( x , z ) = L x + O ( x / L ( 3 ξ ) c )uniformly for x ⩾ 1 , ξ ⩽ z ⩽ x / ξ .
Accelerating Research
Robert Robinson Avenue,
Oxford Science Park, Oxford
OX4 4GP, United Kingdom
Address
John Eccles HouseRobert Robinson Avenue,
Oxford Science Park, Oxford
OX4 4GP, United Kingdom