Corpus ID: 29816631

An Elementary Dyadic Riemann Hypothesis

@article{Knill2018AnED,
  title={An Elementary Dyadic Riemann Hypothesis},
  author={O. Knill},
  journal={ArXiv},
  year={2018},
  volume={abs/1801.04639}
}
  • O. Knill
  • Published 2018
  • Mathematics, Computer Science
  • ArXiv
  • 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
    The counting matrix of a simplicial complex
    2
    Listening to the cohomology of graphs
    • O. Knill
    • Computer Science, Mathematics
    • 2018
    4
    The average simplex cardinality of a finite abstract simplicial complex
    • O. Knill
    • Mathematics, Computer Science
    • 2019
    1
    The hydrogen identity for Laplacians
    • O. Knill
    • Mathematics, Computer Science
    • 2018
    1
    Spectral zeta functions
    1
    The amazing world of simplicial complexes
    9

    References

    Publications referenced by this paper.
    SHOWING 1-10 OF 40 REFERENCES
    One can hear the Euler characteristic of a simplicial complex
    • O. Knill
    • Mathematics, Computer Science
    • 2017
    8
    On Fredholm determinants in topology
    • O. Knill
    • Mathematics, Computer Science
    • 2016
    14
    On a Dehn-Sommerville functional for simplicial complexes
    • O. Knill
    • Mathematics, Computer Science
    • 2017
    8
    The zeta function for circular graphs
    • O. Knill
    • Mathematics, Computer Science
    • 2013
    10
    Cauchy-Binet for Pseudo-Determinants
    28
    Spectral zeta functions of graphs and the Riemann zeta function in the critical strip
    9
    The strong ring of simplicial complexes
    • O. Knill
    • Mathematics, Computer Science
    • 2017
    8
    The graph spectrum of barycentric refinements
    • O. Knill
    • Computer Science, Mathematics
    • 2015
    12
    Generalized hypergeometric series
    669