Numerical computation of the Epstein zeta function.
the exponent parameter as a numeric. See details below.
a vector lattice as a VecLat-class object.
a phase vector or a matrix of phase column vectors.
the stopping criterion for the numerical approximation of the
Epstein zeta function. Default: 3. Increase
a logical or a list.
logical. Should the phase be normalized? Default: TRUE. See details below.
The Epstein zeta function is a multidimensional version of the Riemann zeta function defined as the sum of
for all non-null vectors x of the lattice.
When considered as a function of the phase
Epstein zeta function is invariant under any translation by a lattice
vector. The phase vector
h provided to
Ezeta must lie in
the fundamental tile of the vector lattice
h is automatically normalized.
The algorithm used for computation of the Epstein zeta function is
provided in a paper by Richard E. Crandall, see reference below. In
this implementation, all preliminary computations not depending on
h can be made separately.
prepare is FALSE, the result as a numeric.
prepare is TRUE, preliminary computations not depending on
the phase are returned as a list.
prepare is a list as computed when
prepare is TRUE,
the final result as a numeric.
Crandall, R.E. (1998). Fast evaluation of Epstein zeta functions. Manuscript. http://www.reed.edu/~crandall/papers/epstein.pdf
Loading required package: gsl Loading required package: R2Cuba  2.110572  8.892745
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