Equidistribution and the Riemann hypothesis (Q1344461)

The author outlines the proof of the following theorem: If \(\zeta(s)\) is non-zero for \(\text{Re}(s)\geq 1-2\alpha\), \(0<\alpha< {1\over 4}\), then the sequence \(\{cp^ \alpha- [cp^ \alpha]\}\) is equidistributed for all positive \(c\) and thus, under the stated condition, each digit in the \(j\)-th place after the decimal point in a table of the primes raised to the \(\alpha\)-th powr appears equally often in the average.