An addendum to the paper: “Arithmetic functions over rings with zero divisors” by Ruangsinsap, Laohakosol and P. Udomkavanich.
Ramanujan sums via generalized Möbius functions and applications.
Independence measures of arithmetic functions II
On generalized square-full numbers in an arithmetic progression
Let and . Denote by the set of all integers whose canonical prime representation has all exponents being a multiple of or belonging to the arithmetic progression , . All integers in are called generalized square-full integers. Using the exponent pair method, an upper bound for character sums over generalized square-full integers is derived. An application on the distribution of generalized square-full integers in an arithmetic progression is given.
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