mirror of
https://github.com/vale981/arb
synced 2025-03-06 01:41:39 -05:00
66 lines
1.9 KiB
C
66 lines
1.9 KiB
C
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/*=============================================================================
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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
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it under the terms of the GNU General Public License as published by
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the Free Software Foundation; either version 2 of the License, or
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(at your option) any later version.
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ARB is distributed in the hope that it will be useful,
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but WITHOUT ANY WARRANTY; without even the implied warranty of
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MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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GNU General Public License for more details.
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You should have received a copy of the GNU General Public License
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along with ARB; if not, write to the Free Software
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Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA
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=============================================================================*/
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/******************************************************************************
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Copyright (C) 2016 Pascal Molin
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******************************************************************************/
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#include "acb_dirichlet.h"
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void
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acb_dirichlet_gauss_sum_theta(acb_t res, const acb_dirichlet_group_t G, const acb_dirichlet_char_t chi, slong prec)
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{
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arb_t x;
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acb_t eps;
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arb_init(x);
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if ((G->q == 300 && (chi->n == 271 || chi->n == 131))
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|| (G->q == 600 && (chi->n == 11 || chi->n == 91)))
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{
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/* or could use l'Hopital rule */
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acb_dirichlet_gauss_sum_naive(res, G, chi, prec);
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return;
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}
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arb_one(x);
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acb_dirichlet_chi_theta(res, G, chi, x, prec);
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acb_init(eps);
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acb_conj(eps, res);
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acb_div(eps, res, eps, prec);
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if (chi->parity)
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{
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arb_zero(acb_realref(res));
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arb_sqrt_ui(acb_imagref(res), G->q, prec);
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}
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else
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{
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arb_zero(acb_imagref(res));
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arb_sqrt_ui(acb_realref(res), G->q, prec);
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}
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acb_mul(res, res, eps, prec);
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arb_clear(x);
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acb_clear(eps);
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}
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