mirror of
https://github.com/vale981/arb
synced 2025-03-05 09:21:38 -05:00
76 lines
2.1 KiB
C
76 lines
2.1 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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void
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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)
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{
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slong k;
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acb_t tmp;
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acb_init(tmp);
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acb_one(res);
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/* TODO: efficient subgroup */
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for (k = 0; k < G->num; k++)
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{
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nmod_t pe;
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ulong p, e, ap, bp;
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p = G->P[k].p;
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e = G->P[k].e;
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pe = G->P[k].pe;
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ap = chi1->n % pe.n;
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bp = chi2->n % pe.n;
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if (ap == 1 || bp == 1 || nmod_mul(ap, bp, pe) == 1)
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{
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slong r;
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ulong cond;
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cond = (ap == 1) ? dirichlet_conductor_char(G, chi2) : dirichlet_conductor_char(G, chi1);
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r = jacobi_one_prime(p, e, pe.n, cond);
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/* chi(a,-1) if ap * bp = 1 */
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if (ap != 1 && bp != 1)
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r *= n_jacobi_unsigned(ap, p);
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acb_mul_si(res, res, r, prec);
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}
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else
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{
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dirichlet_group_t Gp;
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dirichlet_char_t chi1p, chi2p;
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dirichlet_group_init(Gp, pe.n);
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dirichlet_char_init(chi1p, Gp);
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dirichlet_char_init(chi2p, Gp);
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chi1p->n = ap;
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chi1p->log[0] = chi1->log[k];
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chi2p->n = ap;
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chi2p->log[0] = chi2->log[k];
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/* TODO: work out gauss relations for e > 1 */
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if (p <= 100 || e > 1)
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acb_dirichlet_jacobi_sum_naive(tmp, Gp, chi1p, chi2p, prec);
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else
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acb_dirichlet_jacobi_sum_gauss(tmp, Gp, chi1p, chi2p, prec);
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acb_mul(res, res, tmp, prec);
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dirichlet_char_clear(chi1p);
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dirichlet_char_clear(chi2p);
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dirichlet_group_clear(Gp);
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}
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}
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acb_clear(tmp);
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}
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