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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"
void
acb_dirichlet_vec_mellin_arb(acb_ptr res, const dirichlet_group_t G, const dirichlet_char_t chi, slong len, const arb_t t, slong n, slong prec)
{
slong k;
arb_t tk, xt, stk, st;
acb_ptr a;
mag_t e;
a = _acb_vec_init(len);
acb_dirichlet_chi_vec(a, G, chi, len, prec);
if (dirichlet_parity_char(G, chi))
{
for (k = 2; k < len; k++)
acb_mul_si(a + k, a + k, k, prec);
}
arb_init(tk);
arb_init(xt);
arb_init(st);
arb_init(stk);
mag_init(e);
arb_sqrt(st, t, prec);
arb_one(tk);
arb_one(stk);
for (k = 0; k < n; k++)
{
_acb_dirichlet_theta_argument_at_arb(xt, G->q, tk, prec);
mag_tail_kexpk2_arb(e, xt, len);
arb_neg(xt, xt);
arb_exp(xt, xt, prec);
/* TODO: reduce len */
acb_dirichlet_qseries_arb(res + k, a, xt, len, prec);
acb_add_error_mag(res + k, e);
acb_mul_arb(res + k, res + k, stk, prec);
arb_mul(tk, tk, t, prec);
arb_mul(stk, stk, st, prec);
}
mag_clear(e);
arb_clear(xt);
arb_clear(tk);
arb_clear(stk);
arb_clear(st);
_acb_vec_clear(a, len);
}
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