Abstract
Let denote the th prime, and consider the function which maps the reciprocals of the positive integers bijectively to the reciprocals of the primes. We show that Hölder continuity of this function is equivalent to a parametrised family of Cramér type estimates on the gaps between successive primes. Here the parametrisation comes from the Hölder exponent. In particular, we show that Cramér’s conjecture is equivalent to the map being Lipschitz. On the other hand, we show that the inverse map is Hölder of all orders but not Lipschitz and this is independent of Cramér’s conjecture.
Citation
Haipeng Chen. Jonathan M. Fraser. "ON HÖLDER MAPS AND PRIME GAPS." Real Anal. Exchange 46 (2) 523 - 532, 2021. https://doi.org/10.14321/realanalexch.46.2.0523
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