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Implement more algorithms for zeta functions #1

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PhilippSchuette opened this issue Feb 20, 2023 · 0 comments
Open

Implement more algorithms for zeta functions #1

PhilippSchuette opened this issue Feb 20, 2023 · 0 comments
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enhancement New feature or request help wanted Extra attention is needed

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@PhilippSchuette
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While being quite straightforward to implement, cycle expansion is not an optimal algorithm for the calculation of (dynamical) zeta functions. This is mainly due to the exponential growth of the number of closed geodesics as their length grows towards infinity.

Thankfully, other algorithms exist: [Bandtlow, Pohl, Schick, Weiße 2020] demonstrated how to calculate zeta functions in their representation as Fredholm determinants. Having such an alternative algorithm available within the PyZeta project could on the one hand enable the calculation of resonances significantly further into the left halfplane. On the other hand one could then verify both methods against each other to gain additional confidence in the validity of the results.

@PhilippSchuette PhilippSchuette added enhancement New feature or request help wanted Extra attention is needed labels Feb 20, 2023
@PhilippSchuette PhilippSchuette self-assigned this Feb 20, 2023
@PhilippSchuette PhilippSchuette added this to the PyZeta Version 1.0.0 milestone Feb 20, 2023
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