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So far, it has been verified that the first complex zeros do, indeed, have real part 1/2 (see ). The important Riemann hypothesis is the unproven conjecture that all these complex zeros have real part 1/2. The zeros occur in conjugate pairs, so if is a zero, then so is. The first three complex zeros of the zeta function are approximately, , and. Where is the complex zero of the Riemann zeta function. This Demonstration uses the following formula to calculate : Snapshot 3: for larger, we need more and more zeta zeros in order to closely match the step function Snapshot 2: the graphs of and the formula using 30 pairs of zeta zeros Snapshot 1: the graphs of the step function and the formula using no zeta zeros
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