H. Shinya

activity

20042009

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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…

A note on gaps

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

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