Description Usage Arguments Details Value References See Also Examples
Numerical computation of the Epstein zeta function.
1 |
s |
the exponent parameter as a numeric. See details below. |
vlat |
a vector lattice as a VecLat-class object. |
h |
a phase vector or a matrix of phase column vectors. |
L |
the stopping criterion for the numerical approximation of the
Epstein zeta function. Default: 3. Increase |
prepare |
a logical or a list. |
norm |
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
exp(-2*pi*I*<h,x>)/|x|^s
for all non-null vectors x of the lattice.
When considered as a function of the phase h
, the
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 vlat
. If norm
is TRUE, 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
the phase h
can be made separately.
If prepare
is FALSE, the result as a numeric.
If prepare
is TRUE, preliminary computations not depending on
the phase are returned as a list.
If 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
VecLat-class
1 2 |
Loading required package: gsl
Loading required package: R2Cuba
[1] 2.110572
[1] 8.892745
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