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/*
Copyright (C) 2016 Pascal Molin
This file is part of Arb.
Arb is free software: you can redistribute it and/or modify it under
the terms of the GNU Lesser General Public License (LGPL) as published
by the Free Software Foundation; either version 2.1 of the License, or
(at your option) any later version. See <http://www.gnu.org/licenses/>.
*/
#include "acb_dirichlet.h"
#include "acb_poly.h"
void
acb_dirichlet_l_vec_hurwitz(acb_ptr res, const acb_t s,
const acb_dirichlet_hurwitz_precomp_t precomp,
const dirichlet_group_t G, slong prec)
{
acb_t a, qs;
acb_ptr zeta, z;
dirichlet_char_t cn;
int deflate;
/* remove pole in Hurwitz zeta at s = 1 */
deflate = acb_is_one(s);
dirichlet_char_init(cn, G);
acb_init(qs);
acb_init(a);
prec += n_clog(G->phi_q, 2);
acb_set_ui(qs, G->q);
acb_neg(a, s);
acb_pow(qs, qs, a, prec);
zeta = z = _acb_vec_init(G->phi_q);
dirichlet_char_one(cn, G);
do {
if (precomp == NULL)
{
acb_set_ui(a, cn->n);
acb_div_ui(a, a, G->q, prec);
if (deflate == 0)
acb_hurwitz_zeta(z, s, a, prec);
else
_acb_poly_zeta_cpx_series(z, s, a, 1, 1, prec);
}
else
{
acb_dirichlet_hurwitz_precomp_eval(z, precomp, cn->n, G->q, prec);
}
acb_mul(z, z, qs, prec);
acb_conj(z, z);
z++;
} while (dirichlet_char_next(cn, G) >= 0);
acb_dirichlet_dft_index(res, zeta, G, prec);
{
slong k;
for (k = 0; k < G->phi_q; k++)
acb_conj(res + k, res + k);
}
/* restore pole for the principal character */
if (deflate)
acb_indeterminate(res);
dirichlet_char_clear(cn);
_acb_vec_clear(zeta, G->phi_q);
acb_clear(qs);
acb_clear(a);
}
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