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- W3036896638 abstract "Let $p_n$ denote the $n$th prime, and consider the function $1/n mapsto 1/p_n$ which maps the reciprocals of the positive integers bijectively to the reciprocals of the primes. We show that Holder continuity of this function is equivalent to a parameterised family of Cram'er type estimates on the gaps between successive primes. Here the parameterisation comes from the Holder exponent. In particular, we show that Cram'er's conjecture is equivalent to the map $1/n mapsto 1/p_n$ being Lipschitz. On the other hand, we show that the inverse map $1/p_n mapsto 1/n$ is Holder of all orders but not Lipshitz and this is independent of Cram'er's conjecture." @default.
- W3036896638 created "2020-06-25" @default.
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- W3036896638 date "2020-06-17" @default.
- W3036896638 modified "2023-10-16" @default.
- W3036896638 title "On Holder maps and prime gaps" @default.
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- W3036896638 doi "https://doi.org/10.48550/arxiv.2006.09947" @default.
- W3036896638 hasPublicationYear "2020" @default.
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