mirror of
https://github.com/vale981/arb
synced 2025-03-05 09:21:38 -05:00
83 lines
2 KiB
C
83 lines
2 KiB
C
/*
|
|
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_zeta_si(acb_t z, slong s, slong prec);
|
|
|
|
/* todo: use euler product for complex s, and check efficiency
|
|
for large negative integers */
|
|
void
|
|
acb_dirichlet_zeta(acb_t res, const acb_t s, slong prec)
|
|
{
|
|
acb_t a;
|
|
double cutoff;
|
|
|
|
if (acb_is_int(s) &&
|
|
arf_cmpabs_2exp_si(arb_midref(acb_realref(s)), FLINT_BITS - 1) < 0)
|
|
{
|
|
acb_zeta_si(res, arf_get_si(arb_midref(acb_realref(s)), ARF_RND_DOWN), prec);
|
|
return;
|
|
}
|
|
|
|
cutoff = 24.0 * prec * sqrt(prec);
|
|
|
|
if (arf_cmpabs_d(arb_midref(acb_imagref(s)), cutoff) >= 0 &&
|
|
arf_cmpabs_d(arb_midref(acb_realref(s)), 10 + prec * 0.1) <= 0)
|
|
{
|
|
acb_dirichlet_zeta_rs(res, s, 0, prec);
|
|
return;
|
|
}
|
|
|
|
acb_init(a);
|
|
acb_one(a);
|
|
|
|
if (arf_sgn(arb_midref(acb_realref(s))) < 0)
|
|
{
|
|
acb_t t, u, v;
|
|
slong wp = prec + 6;
|
|
|
|
acb_init(t);
|
|
acb_init(u);
|
|
acb_init(v);
|
|
|
|
acb_sub_ui(t, s, 1, wp);
|
|
|
|
/* 2 * (2pi)^(s-1) */
|
|
arb_const_pi(acb_realref(u), wp);
|
|
acb_mul_2exp_si(u, u, 1);
|
|
acb_pow(u, u, t, wp);
|
|
acb_mul_2exp_si(u, u, 1);
|
|
|
|
/* sin(pi*s/2) */
|
|
acb_mul_2exp_si(v, s, -1);
|
|
acb_sin_pi(v, v, wp);
|
|
acb_mul(u, u, v, wp);
|
|
|
|
/* gamma(1-s) zeta(1-s) */
|
|
acb_neg(t, t);
|
|
acb_gamma(v, t, wp);
|
|
acb_mul(u, u, v, wp);
|
|
acb_hurwitz_zeta(v, t, a, wp);
|
|
acb_mul(res, u, v, prec);
|
|
|
|
acb_clear(t);
|
|
acb_clear(u);
|
|
acb_clear(v);
|
|
}
|
|
else
|
|
{
|
|
acb_hurwitz_zeta(res, s, a, prec);
|
|
}
|
|
|
|
acb_clear(a);
|
|
}
|
|
|