  Let $N(\sigma,T)$ denote the number of nontrivial zeros of the Riemann zeta
function with real part greater than $\sigma$ and imaginary part between $0$
and $T$. We provide explicit upper bounds for $N(\sigma,T)$ commonly referred
to as a zero density result. In 1937, Ingham showed the following asymptotic
result $N(\sigma,T)=\mathcal{O} ( T^{\frac83(1-\sigma)} (\log T)^5 )$.
Ramar\'{e} recently proved an explicit version of this estimate. We discuss a
generalization of the method used in these two results which yields an explicit
bound of a similar shape while also improving the constants.
