H. Shinya

activity

20042009

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6 papers · 1 filter

math.GM2009

On an arithmetical approach to the Riemann hypothesis

Hisanobu Shinya

In the paper, we first prove a sufficient condition for the Riemann hypothesis which involves the order of magnitude of the partial sum of the Liouville function. Then we show a fo…

math.GM2008

A note on gaps

Hisanobu Shinya

Let $p_{k}$ denote the $k$ -th prime and $d (p_{k}) = p_{k} - p_{k - 1}$ , the difference between consecutive primes. We denote by $N_{ε} (x)$ the number of primes $\leq x$ which satisfy…

math.GM2008

On a certain asymptotic relationship involving $ϑ (t) - ⌊ t ⌋$ and $t^{1/2}$

Hisanobu Shinya

Let $⌊ t ⌋$ denote the greatest positive integer less than or equal to a given positive real number $t$ and $ϑ (t)$ the Chebyshev $ϑ$ -function. In this p…

math.GM2007

On a new approach to the Riemann hypothesis

Hisanobu Shinya

Suppose that the Riemann hypothesis is false and $ρ_{*} = 1/2 + η_{*} + i γ_{*}$ , $η_{*} > 0$ , is a nontrivial zero of the Riemann $ζ$ -function off the critical line. Under the neg…

math.GM2005

A Qualitative Property of the Riemann zeta function

Hisanobu Shinya

The paper was withdrawn by the author. It contained various errors.

math.GM2005

On the Gaps between Two Consecutive Prime Numbers

Hisanobu Shinya

In this article, a relation between a gap $d_{k}$ and divisors of composite numbers between $p_{k}$ and $p_{k + 1}$ is established.

On an arithmetical approach to the Riemann hypothesis

A note on gaps

On a certain asymptotic relationship involving ϑ(t)−⌊t⌋ and t1/2

On a new approach to the Riemann hypothesis

A Qualitative Property of the Riemann zeta function

On the Gaps between Two Consecutive Prime Numbers

On a certain asymptotic relationship involving $ϑ (t) - ⌊ t ⌋$ and $t^{1/2}$