THE PRIMES ARE NOT METRIC POISSONIAN
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Walker, A. (2018). THE PRIMES ARE NOT METRIC POISSONIAN. Mathematika, 64 (1), 230-236. https://doi.org/10.1112/s002557931700050x
It has been known since Vinogradov that, for irrational , the sequence of fractional parts is equidistributed in as ranges over primes. There is a natural second-order equidistribution property, a pair correlation of such fractional parts, which has recently received renewed interest, in particular regarding its relation to additive combinatorics. In this paper we show that the primes do not enjoy this stronger equidistribution property.
The author is supported by EPSRC grant no. EP/M50659X/1.
External DOI: https://doi.org/10.1112/s002557931700050x
This record's URL: https://www.repository.cam.ac.uk/handle/1810/292951