Monthly Archives: March 2012

The Riemann hypothesis: Generalizations of the Riemann hypothesis

For any given mathematical statement, whether it is an established theorem or an unproven conjecture, there is almost always some way to make it “stronger”. One way to make a statement stronger is to make its conclusions more precise. For … Continue reading

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The Riemann hypothesis: The Lindelöf hypothesis

In spite of the strong numerical evidence in favor of the Riemann hypothesis, all attempts to prove it rigorously using techniques of classical analysis have fallen far short. For example, the Hadamard zero-free region actually excludes only a small part … Continue reading

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The Riemann hypothesis: Equivalents of the hypothesis

One reason that the Riemann hypothesis is so important to number theorists is that, as we’ve noted, it implies the smallest possible error estimate in the prime number theorem. In other words, it gives as much information as possible about … Continue reading

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