22 citations · 69 across the 22 of their papers we have counts for
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A new hyperbolicity wedge and a joint semicircle limit for Jensen polynomials of Riemann's -function
Jonathan Holland
Let \[ ξ\!\left(\frac12+z\right) =\sum_{n\geq 0}\frac{γ(n)}{n!}z^{2n}, \qquad J^{d,n}(X) =\sum_{j=0}^{d}\binom djγ(n+j)X^j . \] The Riemann hypothesis is equivalent to the hyperbol…
Reciprocity and the Maslov Phase
Jonathan Holland
We give a metaplectic proof of Hilbert reciprocity, and hence of quadratic reciprocity, in which the local phase is the Kashiwara--Maslov phase of a triple of Lagrangians. In rank…
Triality and the Magic Square of Hans Freudenthal
Jonathan Holland, George Sparling
We study real triality structures through their intrinsic tensor algebra. Starting from a single triality symbol, we construct the associated Lie algebra of two-triality operators,…
Sachs Equations and Plane Waves VI: Penrose Limits
Jonathan Holland, George Sparling
Let be a Lorentzian manifold whose local space of unparametrized null geodesics is smooth. We show that its Penrose limits assemble into a smooth bundle of pla…
Sachs Equations and Plane Waves, V: Ward, Fourier, and Heisenberg Symmetry on Plane Waves
Jonathan Holland, George Sparling
This article studies wave equations and their solutions on plane wave spacetimes of arbitrary dimension, developing the interplay among three structural layers: the Ward progressin…