1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
|
/*
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"
void
acb_dirichlet_l_hurwitz(acb_t res, const acb_t s,
const acb_dirichlet_hurwitz_precomp_t precomp,
const dirichlet_group_t G, const dirichlet_char_t chi, slong prec)
{
ulong order, chin, mult;
acb_t t, u, a, w;
dirichlet_char_t cn;
acb_dirichlet_roots_t roots;
int deflate;
/* remove pole in Hurwitz zeta at s = 1 */
deflate = 0;
if (acb_is_one(s))
{
if (dirichlet_char_is_principal(G, chi))
{
acb_indeterminate(res);
return;
}
deflate = 1;
}
dirichlet_char_init(cn, G);
acb_init(t);
acb_init(u);
acb_init(a);
acb_init(w);
dirichlet_char_one(cn, G);
acb_zero(t);
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);
do {
chin = dirichlet_pairing_char(G, chi, cn) / mult;
if (precomp == NULL)
{
acb_set_ui(a, cn->n);
acb_div_ui(a, a, G->q, prec);
if (deflate == 0)
acb_hurwitz_zeta(u, s, a, prec);
else
_acb_poly_zeta_cpx_series(u, s, a, 1, 1, prec);
}
else
{
acb_dirichlet_hurwitz_precomp_eval(u, precomp, cn->n, G->q, prec);
}
acb_dirichlet_root(w, roots, chin, prec);
acb_addmul(t, u, w, prec);
} while (dirichlet_char_next(cn, G) >= 0);
acb_set_ui(u, G->q);
acb_neg(a, s);
acb_pow(u, u, a, prec);
acb_mul(res, t, u, prec);
dirichlet_char_clear(cn);
acb_dirichlet_roots_clear(roots);
acb_clear(t);
acb_clear(u);
acb_clear(a);
acb_clear(w);
}
|
