A relation to a remainder terms in an asymptotic formula for the associated Euler totient function

2025/05/25 by Iwata, Hideto
#FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2505.19344

Abstract

H.L.Montgomery proved a relation for error terms in asymptotic formulas for the Euler totient function. J.Kaczorowski defined the associated Euler totient function which generalizes and obtained an asymptotic formula for it. In this paper, we prove a relation on error terms similar to H.L.Montgomery's result for a certain special case of the associated Euler totient function.

Citations

• An analytic approach to the remainder terms in the asymptotic formulas -- the Volterra integral equation, the Whittaker function

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