| 1. | Where is the th Bernoulli number and is the Riemann zeta function.
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| 2. | This shows that the zeta function is a rational function of t.
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| 3. | A fundamental property of the Riemann zeta function is its functional equation:
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| 4. | The picture shows three zeros of the zeta function, at about, and.
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| 5. | This operator also has a continuous spectrum consisting of the Hurwitz zeta function.
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| 6. | The zeta function is a rational function in " T ".
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| 7. | Here denotes the Riemann zeta function and ? the imaginary unit.
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| 8. | In zeta function, one of which is the well-known Riemann hypothesis.
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| 9. | More advanced methods are required, such as zeta function regularization or Ramanujan summation.
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| 10. | Where the sum extends over ?, the non-trivial zeros of the zeta function.
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