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Caroline Turnage-Butterbaugh : Gaps between zeros of the Riemann zeta-function on the critical line

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The Riemann Hypothesis is the conjecture that all nontrivial zeros of the Riemann zeta-function have real part equal to 1/2, and its truth would provide, for example, information about the distribution of the primes. Certain knowledge about the vertical distribution of the zeros of the Riemann zeta-function would also have striking consequences. I will motivate the study of the zeros of the Riemann zeta-function and discuss the methods used to study the vertical distribution of its nontrivial zeros. We will end with a discussion of current joint work with Brian Conrey concerning gaps between the nontrivial zeros of the Riemann zeta-function.

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