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Published June 12, 2018 | Submitted
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An effective universality theorem for the Riemann zeta-function


Let 00, once T is large enough. This was refined by Bagchi who showed that the measure of such t∈[0,T] is (c(ε)+o(1))T, for all but at most countably many ε>0. Using a completely different approach, we obtain the first effective version of Voronin's Theorem, by showing that in the rate of convergence one can save a small power of the logarithm of T. Our method is flexible, and can be generalized to other L-functions in the t-aspect, as well as to families of L-functions in the conductor aspect.

Additional Information

The first and third authors are partially supported by Discovery Grants from the Natural Sciences and Engineering Research Council of Canada.

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Submitted - 1611.10325.pdf


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