7 papers
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…
A note on gaps
Hisanobu Shinya
Let denote the -th prime and , the difference between consecutive primes. We denote by the number of primes which satisfy…
On a certain asymptotic relationship involving and
Hisanobu Shinya
Let denote the greatest positive integer less than or equal to a given positive real number and the Chebyshev -function. In this p…
On a new approach to the Riemann hypothesis
Hisanobu Shinya
Suppose that the Riemann hypothesis is false and , , is a nontrivial zero of the Riemann -function off the critical line. Under the neg…
A Qualitative Property of the Riemann zeta function
Hisanobu Shinya
The paper was withdrawn by the author. It contained various errors.
On the Gaps between Two Consecutive Prime Numbers
Hisanobu Shinya
In this article, a relation between a gap and divisors of composite numbers between and is established.
On a method for obtaining a planar region with two equichordal points
Hisanobu Shinya
This paper has been withdrawn by the author. It has been shown by G.A. Edgar that curves created by the presented method are not continuous at θ= 0. See http://www.math.ohio-state.…