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

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 $t^{1/2}$.

arXiv commentWithdrawn; this work is completely nonsense