Sometime ago, I read somewhere (should be in Titschmarsh) that, if $N(\sigma, T)$ denotes the number of zeros of the Riemann zeta function $\zeta(s)$ with $\Re(s)\geq \sigma>1/2$ up to height $T>0$, then some result of Ingham says $$N(\sigma, T)\ll T^{\frac{3(1-\sigma)}{2-\sigma}}\log^{5}T.$$


Where can I find a proof of this result? A Google search didn't yield much.



Where can I find this result of Ingham?
According to Titchmarsh p.236, the result appears in


Ingham, A. E.
On the estimation of N(σ,T).
Quart. J. Math., Oxford Ser. 11, (1940). 291–292.


Link: <https://doi.org/10.1093/qmath/os-11.1.201>


