# Zeros of Lattice Sums: 2. A Geometry for the Generalised Riemann Hypothesis

@article{McPhedran2016ZerosOL, title={Zeros of Lattice Sums: 2. A Geometry for the Generalised Riemann Hypothesis}, author={Ross C. McPhedran}, journal={arXiv: Mathematical Physics}, year={2016} }

The location of zeros of the basic double sum over the square lattice is studied. This sum can be represented in terms of the product of the Riemann zeta function and the Dirichlet beta function, so that the assertion that all its non-trivial zeros lie on the critical line is a particular case of the Generalised Riemann Hypothesis (GRH). It is shown that a new necessary and sufficient condition for this special case of the GRH to hold is that a particular set of equimodular and equiargument…

## One Citation

### Zeros of Lattice Sums: 3. Reduction of the Generalised Riemann Hypothesis to Specific Geometries

- Mathematics
- 2016

The location of zeros of the basic double sum over the square lattice is studied. This sum can be represented in terms of the product of the Riemann zeta function and the Dirichlet beta function, so…

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