An Asymptotic Formula for the Chebyshev Theta Function

Aditya Ghosh

Let $\{p_n{\}}_{n\ge 1}$ be the sequence of primes and $\vartheta (x)={\sum }_{p\le x}\log p$, where $p$ runs over the primes not exceeding $x$, be the Chebyshev $\vartheta$-functio…