A positive algebraic irrational number is normal to base b if and only if a certain averaged sum of Riemann zeta values over vertical arithmetic progressions vanishes for every integer k≥0.
Bailey, Jonathan M
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Normality of algebraic numbers and the Riemann zeta function
A positive algebraic irrational number is normal to base b if and only if a certain averaged sum of Riemann zeta values over vertical arithmetic progressions vanishes for every integer k≥0.