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Average distribution of k ‐free numbers in arithmetic progressions
Author(s) -
Liu Kui,
Shparlinski Igor E.,
Zhang Tianping
Publication year - 2020
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.201900006
Subject(s) - mathematics , arithmetic , asymptotic formula , value (mathematics) , discrete mathematics , combinatorics , statistics
We obtain a new bound on the average value of the error term in the asymptotic formula for the number of k ‐free numbers in arithmetic progressions. In particular, we improve the results of J. Gibson (2014) and C. Hooley (1975).