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/*
Copyright (C) 2016 Fredrik Johansson
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"
/* todo: move implemetation to the acb_dirichlet module */
void _acb_poly_zeta_cpx_reflect(acb_ptr t, const acb_t h,
const acb_t a, int deflate, slong len, slong prec);
void
acb_dirichlet_l_jet(acb_ptr res, const acb_t s,
const dirichlet_group_t G, const dirichlet_char_t chi,
int deflate, slong len, slong prec)
{
ulong order, chin, mult, phi;
acb_t a, w;
acb_ptr t, u;
dirichlet_char_t cn;
acb_dirichlet_roots_t roots;
int deflate_hurwitz;
if (len <= 0)
return;
/* special-case Riemann zeta */
if (G == NULL || G->q == 1)
{
if (len == 1 && !deflate)
acb_dirichlet_zeta(res, s, prec);
else
acb_dirichlet_zeta_jet(res, s, deflate, len, prec);
return;
}
if (len == 1 && !(deflate && dirichlet_char_is_principal(G, chi)))
{
acb_dirichlet_l(res, s, G, chi, prec);
return;
}
if (dirichlet_char_is_principal(G, chi))
deflate_hurwitz = deflate;
else
deflate_hurwitz = acb_is_one(s);
dirichlet_char_init(cn, G);
t = _acb_vec_init(len);
u = _acb_vec_init(len + 2);
acb_init(a);
acb_init(w);
dirichlet_char_one(cn, G);
prec += n_clog(G->phi_q, 2);
order = dirichlet_order_char(G, chi);
mult = G->expo / order;
acb_dirichlet_roots_init(roots, order, dirichlet_group_size(G), prec);
phi = 0;
do
{
chin = dirichlet_pairing_char(G, chi, cn) / mult;
acb_set_ui(a, cn->n);
acb_div_ui(a, a, G->q, prec);
_acb_poly_zeta_cpx_series(u, s, a, deflate_hurwitz, len, prec);
acb_dirichlet_root(w, roots, chin, prec);
_acb_vec_scalar_addmul(t, u, len, w, prec);
phi++;
}
while (dirichlet_char_next(cn, G) >= 0);
if (dirichlet_char_is_principal(G, chi) && deflate)
{
/* res = t * q^(-(s+x)) + [phi(q) * (q^(-(s+x)) - q^-1) / ((s+x)-1)] */
if (acb_is_one(s))
{
acb_set_ui(a, G->q);
_acb_poly_acb_invpow_cpx(u, a, s, len + 1, prec);
_acb_poly_mullow(res, t, len, u, len, len, prec);
acb_set_ui(u, phi);
_acb_vec_scalar_addmul(res, u + 1, len, u, prec);
}
else
{
acb_sub_ui(u, s, 1, prec);
acb_one(u + 1);
acb_set_ui(a, G->q);
_acb_poly_acb_invpow_cpx(u + 2, a, s, len, prec);
_acb_poly_mullow(res, t, len, u + 2, len, len, prec);
acb_inv(a, a, prec);
acb_sub(u + 2, u + 2, a, prec);
_acb_poly_div_series(t, u + 2, len, u, 2, len, prec);
acb_set_ui(u, phi);
_acb_vec_scalar_addmul(res, t, len, u, prec);
}
}
else
{
/* res = t * q^(-(s+x)) */
acb_set_ui(a, G->q);
_acb_poly_acb_invpow_cpx(u, a, s, len, prec);
_acb_poly_mullow(res, t, len, u, len, len, prec);
}
dirichlet_char_clear(cn);
acb_dirichlet_roots_clear(roots);
_acb_vec_clear(t, len);
_acb_vec_clear(u, len + 2);
acb_clear(a);
acb_clear(w);
}
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