# An Elementary Dyadic Riemann Hypothesis

@article{Knill2018AnED, title={An Elementary Dyadic Riemann Hypothesis}, author={O. Knill}, journal={ArXiv}, year={2018}, volume={abs/1801.04639} }

The connection zeta function of a finite abstract simplicial complex G is defined as zeta_L(s)=sum_x 1/lambda_x^s, where lambda_x are the eigenvalues of the connection Laplacian L defined by L(x,y)=1 if x and y intersect and 0 else. (I) As a consequence of the spectral formula chi(G)=sum_x (-1)^dim(x) = p(G)-n(G), where p(G) is the number of positive eigenvalues and n(G) is the number of negative eigenvalues of L, both the Euler characteristic chi(G)=zeta(0)-2 i zeta'(0)/pi as well as… CONTINUE READING

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The average simplex cardinality of a finite abstract simplicial complex

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