6 papers · 1 filter
On a relation to the Riemann Hypothesis and an analytic part for the divisor function
Hideto Iwata
Let phi(n) denote the Euler totient function. We study the analytic part associated with the summatory function of sigma_1(n) and obtain explicit bounds under the Riemann Hypothesi…
A relation to a remainder terms in an asymptotic formula for the associated Euler totient function
Hideto Iwata
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 generalize…
An analytic approach to the remainder terms in the asymptotic formulas -- the Volterra integral equation, the Whittaker function
Hideto Iwata
In the present paper, firstly, we consider the Volterra integral equation of second type for a remainder term in an asymptotic formula of an arithmetic function which satisfies som…
On some analytic properties of a function associated with the Selberg class satisfying certain special conditions
Hideto Iwata
In 2001, M.Rekos described the analytic behavior for a function connected with the Euler totient function for Im (see (1.2)) imitating the previous research of [1] an…
On the solution of the Volterra integral equation of second type for the error term in an asymptotic formula for arithmetical functions
Hideto Iwata
This paper, we first consider the pair of complex-valued arithmetical functions (a(n),b(n)) satisfying. We prove that the solution of the Volterra integral equation of second type…
On the Volterra integral equation for the remainder term in the asymptotic formula on the associated Euler totient function
Hideto Iwata
This paper, first, we consider the Volterra integral equation for the remainder term in the asymptotic formula for the associated Euler totient function. Secondly, we solve the Vol…