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https://github.com/vale981/arb
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38 lines
1.1 KiB
C
38 lines
1.1 KiB
C
/*
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Copyright (C) 2016 Pascal Molin
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This file is part of Arb.
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Arb is free software: you can redistribute it and/or modify it under
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the terms of the GNU Lesser General Public License (LGPL) as published
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by the Free Software Foundation; either version 2.1 of the License, or
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(at your option) any later version. See <http://www.gnu.org/licenses/>.
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*/
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#include "acb_dirichlet.h"
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/* should use only for prime power modulus */
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void
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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)
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{
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/* J_q(a,b)G_q(ab) = G_q(a)G_q(b) */
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acb_t tmp;
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dirichlet_char_t chi12;
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dirichlet_char_init(chi12, G);
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dirichlet_char_mul(chi12, G, chi1, chi2);
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acb_init(tmp);
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acb_dirichlet_gauss_sum(res, G, chi1, prec);
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if (chi2->n == chi1->n)
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acb_set(tmp, res);
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else
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acb_dirichlet_gauss_sum(tmp, G, chi2, prec);
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acb_mul(res, res, tmp, prec);
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acb_dirichlet_gauss_sum(tmp, G, chi12, prec);
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acb_div(res, res, tmp, prec);
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dirichlet_char_clear(chi12);
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acb_clear(tmp);
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}
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