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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"
/* should use only for prime power modulus */
void
acb_dirichlet_jacobi_sum_gauss(acb_t res, const dirichlet_group_t G, const dirichlet_char_t chi1, const dirichlet_char_t chi2, slong prec)
{
/* J_q(a,b)G_q(ab) = G_q(a)G_q(b) */
acb_t tmp;
dirichlet_char_t chi12;
dirichlet_char_init(chi12, G);
dirichlet_char_mul(chi12, G, chi1, chi2);
acb_init(tmp);
acb_dirichlet_gauss_sum(res, G, chi1, prec);
if (chi2->n == chi1->n)
acb_set(tmp, res);
else
acb_dirichlet_gauss_sum(tmp, G, chi2, prec);
acb_mul(res, res, tmp, prec);
acb_dirichlet_gauss_sum(tmp, G, chi12, prec);
acb_div(res, res, tmp, prec);
dirichlet_char_clear(chi12);
acb_clear(tmp);
}
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