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An addendum to the paper: “Arithmetic functions over rings with zero divisors” by Ruangsinsap, Laohakosol and P. Udomkavanich.

Narkiewicz, Władysław; Ruengsinsub, Pattira; Laohakosol, Vichian — 2004

Bulletin of the Malaysian Mathematical Sciences Society. Second Series

Ramanujan sums via generalized Möbius functions and applications.

Laohakosol, Vichian; Ruengsinsub, Pattira; Pabhapote, Nittiya — 2006

International Journal of Mathematics and Mathematical Sciences

Independence measures of arithmetic functions II

Takao Komatsu; Vichian Laohakosol; Pattira Ruengsinsub — 2012

Acta Arithmetica

On generalized square-full numbers in an arithmetic progression

Angkana Sripayap; Pattira Ruengsinsub; Teerapat Srichan — 2022

Czechoslovak Mathematical Journal

Let $a$ and $b \in ℕ$ . Denote by $R_{a, b}$ the set of all integers $n > 1$ whose canonical prime representation $n = p_{1}^{α_{1}} p_{2}^{α_{2}} \dots p_{r}^{α_{r}}$ has all exponents $α_{i}$ $(1 \leq i \leq r)$ being a multiple of $a$ or belonging to the arithmetic progression $a t + b$ , $t \in ℕ_{0} : = ℕ \cup {0}$ . All integers in $R_{a, b}$ 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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