Number Theory Seminar
Wednesday, November 2, 2016, 1:30pm, 119 Physics
William D. Banks (University of Missouri)
Consecutive primes and Beatty sequences
Abstract:
Beatty sequences are generalized arithmetic progressions which have been studied intensively in recent years. Thanks to the work of Vinogradov, it is known that every Beatty sequence S contains "appropriately many" prime numbers. For a given pair of Beatty sequences S and T, it is natural to wonder whether there are "appropriately many" primes in S for which the next larger prime lies in T. In this talk, I will show that this is indeed the case if one assumes a certain strong form of the Hardy-Littlewood conjectures. This is recent joint work with Victor Guo. [video]

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