Ramanujan's lattice point problem, prime number theory and other remarks.
Ramanujan's lattice point problem, prime number theory and other remarks.
This paper gives results on four diverse topics. The first result is that the error term for the number of integers $2^u3^v \le n$ is $O((\log n)^{1-\delta})$ with $\delta=(2^{40}(\log3))^{-1}$, using a theorem of A. Baker and G. W\"ustholz. The second result is an averaged explicit formula \[ \psi(x) = x-\frac{1}{T} …