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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_jacobi_sum_factor(acb_t res, const dirichlet_group_t G, const dirichlet_char_t chi1, const dirichlet_char_t chi2, slong prec)
{
slong k;
acb_t tmp;
acb_init(tmp);
acb_one(res);
/* TODO: efficient subgroup */
for (k = 0; k < G->num; k++)
{
nmod_t pe;
ulong p, e, ap, bp;
p = G->P[k].p;
e = G->P[k].e;
pe = G->P[k].pe;
ap = chi1->n % pe.n;
bp = chi2->n % pe.n;
if (ap == 1 || bp == 1 || nmod_mul(ap, bp, pe) == 1)
{
slong r;
ulong cond;
cond = (ap == 1) ? dirichlet_conductor_char(G, chi2) : dirichlet_conductor_char(G, chi1);
r = jacobi_one_prime(p, e, pe.n, cond);
/* chi(a,-1) if ap * bp = 1 */
if (ap != 1 && bp != 1)
r *= n_jacobi_unsigned(ap, p);
acb_mul_si(res, res, r, prec);
}
else
{
dirichlet_group_t Gp;
dirichlet_char_t chi1p, chi2p;
dirichlet_group_init(Gp, pe.n);
dirichlet_char_init(chi1p, Gp);
dirichlet_char_init(chi2p, Gp);
chi1p->n = ap;
chi1p->log[0] = chi1->log[k];
chi2p->n = ap;
chi2p->log[0] = chi2->log[k];
/* TODO: work out gauss relations for e > 1 */
if (p <= 100 || e > 1)
acb_dirichlet_jacobi_sum_naive(tmp, Gp, chi1p, chi2p, prec);
else
acb_dirichlet_jacobi_sum_gauss(tmp, Gp, chi1p, chi2p, prec);
acb_mul(res, res, tmp, prec);
dirichlet_char_clear(chi1p);
dirichlet_char_clear(chi2p);
dirichlet_group_clear(Gp);
}
}
acb_clear(tmp);
}
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