Achim Kempf, Department of Applied Mathematics, University of Waterloo
"Amplified foreshadowing of jumping champions"
Successive jumping champions, conjectured to be primorials, arise for exceedingly large numbers. To some extent, the presence of jumping champions is foreshadowed in much smaller sets of primes, namely, for example, in histograms of all (i.e., not just nearest-neighbor) prime distances and also in the Fourier analysis of the distribution of primes. Here, we apply new methods from information theory to the study of the distribution of primes. Technically, the new methods are based on von Neumann's theory of self-adjoint extensions of symmetric operators and they also relate to the theory of Hardy spaces. We find that the new methods amplify the foreshadowing of large jumping champions.
MC
6486*
*NB:
not
the
usual
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