epsteinZeta.c File Reference

Calculates the (regularized) Epstein zeta function and the (regularized) anisotropic Epstein zeta function. More...

#include <complex.h>
#include <stdbool.h>
#include "epsteinZeta.h"
#include "zeta.h"

Include dependency graph for epsteinZeta.c:

Functions
double complex	epsteinZeta (double nu, unsigned int dim, const double *a, const double *x, const double *y)
	calculates the Epstein zeta function.
double complex	epsteinZetaReg (double nu, unsigned int dim, const double *a, const double *x, const double *y)
	calculates the regularized Epstein zeta function.
double complex	epsteinZetaAniso (double nu, unsigned int dim, const double *a, const double *x, const double *y, const unsigned int *alpha)
	calculates the anisotropic Epstein zeta function.
double complex	epsteinZetaAnisoReg (double nu, unsigned int dim, const double *a, const double *x, const double *y, const unsigned int *alpha)
	calculates the regularized anisotropic Epstein zeta function.

Detailed Description

Calculates the (regularized) Epstein zeta function and the (regularized) anisotropic Epstein zeta function.

Author

Andreas Buchheit, Jonathan Busse and Ruben Gutendorf.

See also

Buchheit, A. A., Busse, J. K., & Gutendorf, R. (2026). "Computation and properties of the Epstein zeta function with applications to quantum systems." IMA Journal of Numerical Analysis, drag057. DOI: 10.1093/imanum/drag057 *

Author

Andreas Buchheit, Jonathan Busse and Ruben Gutendorf.

Date

06/13/2024

Function Documentation

epsteinZeta()

double complex epsteinZeta	(	double	nu,
		unsigned int	dim,
		const double *	a,
		const double *	x,
		const double *	y )

calculates the Epstein zeta function.

Parameters

[in]	nu	exponent for the Epstein zeta function.
[in]	dim	dimension of the input vectors.
[in]	a	matrix that transforms the lattice.
[in]	x	shift vector.
[in]	y	wavevector.

Returns

function value of the Epstein zeta function.

epsteinZetaAniso()

double complex epsteinZetaAniso	(	double	nu,
		unsigned int	dim,
		const double *	a,
		const double *	x,
		const double *	y,
		const unsigned int *	alpha )

calculates the anisotropic Epstein zeta function.

Parameters

[in]	nu	exponent for the Epstein zeta function.
[in]	dim	dimension of the input vectors.
[in]	a	matrix that transforms the lattice.
[in]	x	shift vector.
[in]	y	wavevector.
[in]	alpha	multiindex for the anisotropy.

Returns

function value of the anisotropic Epstein zeta function.

epsteinZetaAnisoReg()

double complex epsteinZetaAnisoReg	(	double	nu,
		unsigned int	dim,
		const double *	a,
		const double *	x,
		const double *	y,
		const unsigned int *	alpha )

calculates the regularized anisotropic Epstein zeta function.

Parameters

[in]	nu	exponent for the Epstein zeta function.
[in]	dim	dimension of the input vectors.
[in]	a	matrix that transforms the lattice.
[in]	x	shift vector.
[in]	y	wavevector.
[in]	alpha	multiindex for the anisotropy.

Returns

function value of the regularized anisotropic Epstein zeta function.

epsteinZetaReg()

double complex epsteinZetaReg	(	double	nu,
		unsigned int	dim,
		const double *	a,
		const double *	x,
		const double *	y )

calculates the regularized Epstein zeta function.

Parameters

[in]	nu	exponent for the Epstein zeta function.
[in]	dim	dimension of the input vectors.
[in]	a	matrix that transforms the lattice.
[in]	x	shift vector.
[in]	y	wavevector.

Returns

function value of the regularized Epstein zeta function.