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/*
Copyright (C) 2016 Fredrik Johansson
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_hardy_z(acb_ptr res, const acb_t t,
const dirichlet_group_t G, const dirichlet_char_t chi,
slong len, slong prec)
{
acb_ptr v, w;
slong k;
int is_real;
if (len <= 0)
return;
/* use reflection formula -- todo for other characters */
if ((G == NULL || G->q == 1) && arf_sgn(arb_midref(acb_imagref(t))) > 0)
{
acb_neg(res, t);
acb_dirichlet_hardy_z(res, res, G, chi, len, prec);
for (k = 1; k < len; k += 2)
acb_neg(res + k, res + k);
return;
}
v = _acb_vec_init(len);
w = _acb_vec_init(len);
is_real = acb_is_real(t);
/* v = exp(i theta(t+x)) */
acb_dirichlet_hardy_theta(v, t, G, chi, len, prec);
_acb_vec_scalar_mul_onei(v, v, len);
_acb_poly_exp_series(v, v, len, len, prec);
/* w = L(1/2 + i (t+x)) */
acb_one(w);
acb_mul_2exp_si(w, w, -1);
arb_sub(acb_realref(w), acb_realref(w), acb_imagref(t), prec);
arb_set(acb_imagref(w), acb_realref(t));
acb_dirichlet_l_jet(w, w, G, chi, 0, len, prec);
for (k = 0; k < len; k++)
{
if (k % 4 == 1)
acb_mul_onei(w + k, w + k);
else if (k % 4 == 2)
acb_neg(w + k, w + k);
else if (k % 4 == 3)
acb_div_onei(w + k, w + k);
}
_acb_poly_mullow(res, v, len, w, len, len, prec);
if (is_real)
for (k = 0; k < len; k++)
arb_zero(acb_imagref(res + k));
_acb_vec_clear(v, len);
_acb_vec_clear(w, len);
}
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