On a certain asymptotic relationship involving $\vartheta(t) - \lfloor t \rfloor$ and $t^{1/2}$

Hisanobu Shinya

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arXiv · 0806.1571

On a certain asymptotic relationship involving $\vartheta(t) - \lfloor t \rfloor$ and $t^{1/2}$

Hisanobu Shinya

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Abstract

Let $\lfloor t \rfloor$ denote the greatest positive integer less than or equal to a given positive real number $t$ and $\vartheta(t)$ the Chebyshev $\vartheta$-function. In this paper, we prove a certain asymptotic relationship involving $\vartheta(t) - \lfloor t \rfloor $ and $t^{1/2}$.

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BibTeX RIS

Hisanobu Shinya. 2011-09-11. On a certain asymptotic relationship involving $\vartheta(t) - \lfloor t \rfloor$ and $t^{1/2}$. https://arxiv.org/abs/0806.1571

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