45 citations · 674 across the 102 of their papers we have counts for
6 papers · 1 filter
On Fredholm determinants in topology
Oliver Knill
Given an abstract simplicial complex G, the connection graph G' of G has as vertex set the faces of the complex and connects two if they intersect. If A is the adjacency matrix of…
On Particles and Primes
Oliver Knill
Primes in the two complete associative normed division algebras C and H have affinities with structures seen in the standard model of particle physics. On the integers in the two a…
On Primes, Graphs and Cohomology
Oliver Knill
The counting function on the natural numbers defines a discrete Morse-Smale complex with a cohomology for which topological quantities like Morse indices, Betti numbers or counting…
Some experiments in number theory
Oliver Knill
We experiment with some topics in elementary number theory. For matrices defined by Gaussian primes we observe a circular spectral law for the eigenvalues. We look at matrices defi…
Goldbach for Gaussian, Hurwitz, Octavian and Eisenstein primes
Oliver Knill
We formulate Goldbach type questions for Gaussian, Hurwitz, Octavian and Eisenstein primes. They are different from Goldbach type statements by Takayoshi Mitsui from 1960 for numbe…
Gauss-Bonnet for multi-linear valuations
Oliver Knill
We prove Gauss-Bonnet and Poincare-Hopf formulas for multi-linear valuations on finite simple graphs G=(V,E) and answer affirmatively a conjecture of Gruenbaum from 1970 by constru…