series for it is known as Gram series. Because for all , this series converges for all positive by comparison with the series for . The logarithm in the Gram series of the sum over the non-trivial zero contribution should be evaluated as and not .

Folkmar Bornemann proved, when assuming the conjecture that all zeros of the Riemann zeta function are simple, that
:where runs over the non-trivial zeros of the Riemann zeta function and .

The

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