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
|
/*
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_root_number_theta(acb_t res, const dirichlet_group_t G, const dirichlet_char_t chi, slong prec)
{
arb_t x;
acb_t eps;
arb_init(x);
arb_one(x);
acb_dirichlet_theta_arb(res, G, chi, x, prec);
acb_init(eps);
acb_conj(eps, res);
acb_div(res, res, eps, prec);
arb_clear(x);
acb_clear(eps);
}
void
acb_dirichlet_root_number(acb_t res, const dirichlet_group_t G, const dirichlet_char_t chi, slong prec)
{
if (dirichlet_conductor_char(G, chi) < G->q)
{
flint_printf("root number: need primitive character\n");
flint_abort();
}
else if (G->num > 1)
{
acb_t iq;
acb_init(iq);
acb_dirichlet_gauss_sum_order2(iq, G, chi, prec);
acb_dirichlet_gauss_sum(res, G, chi, prec);
acb_div(res, res, iq, prec);
acb_clear(iq);
}
else
{
acb_dirichlet_root_number_theta(res, G, chi, prec);
}
}
|
