# Where can I find this result of Ingham?

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.

• Results of this type are called zero-density theorems, if you want to look for further developments. – Greg Martin Feb 9 '19 at 0:48

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.