Pair correlation and twin primes revisited
We establish a connection between the conjectural two-over-two ratios formula for the Riemann zetafunction and a conjecture concerning correlations of a certain arithmetic function. Specifically, we prove that the ratios conjecture and the arithmetic correlations conjecture imply the same result. Th...
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| Format: | Journal article |
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Royal Society
2016
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| Summary: | We establish a connection between the conjectural two-over-two ratios formula for the Riemann zetafunction and a conjecture concerning correlations of a certain arithmetic function. Specifically, we prove that the ratios conjecture and the arithmetic correlations conjecture imply the same result. This casts a new light on the underpinnings of the ratios conjecture, which previously had been motivated by analogy with formulae in random matrix theory and by a heuristic recipe. |
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