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math.NT2026
On the asymptotic behavior of the integral T(x)
Mihoub Bouderbala, Meselem Karras
In this paper, we estimate the integral T(x) mentioned in the title, where {t} denotes the fractional part of the real number t, and x is any positive real number.
math.NT2026
On the Mean Value of a Weighted Composite Arithmetic Function
Mihoub Bouderbala
The primary objective of this paper is to employ methods from analytic number theory to investigate the mean value properties of a composite function involving the Dirichlet diviso…