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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"
void
acb_dirichlet_powsum_term(acb_ptr res, arb_t log_prev, ulong * prev,
const acb_t s, ulong k, int integer, int critical_line, slong len, slong prec)
{
slong i;
if (integer)
{
arb_neg(acb_realref(res), acb_realref(s));
arb_set_ui(acb_imagref(res), k);
arb_pow(acb_realref(res), acb_imagref(res), acb_realref(res), prec);
arb_zero(acb_imagref(res));
if (len != 1)
{
arb_log_ui_from_prev(log_prev, k, log_prev, *prev, prec);
*prev = k;
}
}
else
{
arb_t w;
arb_init(w);
arb_log_ui_from_prev(log_prev, k, log_prev, *prev, prec);
*prev = k;
arb_mul(w, log_prev, acb_imagref(s), prec);
arb_sin_cos(acb_imagref(res), acb_realref(res), w, prec);
arb_neg(acb_imagref(res), acb_imagref(res));
if (critical_line)
{
arb_rsqrt_ui(w, k, prec);
acb_mul_arb(res, res, w, prec);
}
else
{
arb_mul(w, acb_realref(s), log_prev, prec);
arb_neg(w, w);
arb_exp(w, w, prec);
acb_mul_arb(res, res, w, prec);
}
arb_clear(w);
}
if (len > 1)
{
arb_neg(log_prev, log_prev);
for (i = 1; i < len; i++)
{
acb_mul_arb(res + i, res + i - 1, log_prev, prec);
acb_div_ui(res + i, res + i, i, prec);
}
arb_neg(log_prev, log_prev);
}
}
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