mirror of
https://github.com/vale981/arb
synced 2025-03-04 17:01:40 -05:00
109 lines
2.9 KiB
C
109 lines
2.9 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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/* J_N(1,a) = sum on x = 1 mod some p | q */
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ulong
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jacobi_one_prime(ulong p, ulong e, ulong pe, ulong cond)
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{
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if (e > 1 && cond % (p*p) == 0)
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{
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return 0;
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}
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else
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{
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slong r = (e > 1) ? pe / p : 1;
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if (cond % p)
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return r * (p - 2);
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else
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return -r;
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}
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}
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static ulong
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jacobi_one(const dirichlet_group_t G, ulong cond)
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{
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slong k, r = 1;
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for (k = 0; k < G->num; k++)
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r *= jacobi_one_prime(G->P[k].p, G->P[k].e,
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G->P[k].pe.n, cond);
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return r;
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}
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void
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acb_dirichlet_jacobi_sum(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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if (G->q_even > 1)
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{
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acb_zero(res);
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}
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else if (chi1->n == 1 || chi2->n == 1)
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{
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ulong cond = (chi1->n == 1) ? dirichlet_conductor_char(G, chi2) : dirichlet_conductor_char(G, chi1);
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acb_set_si(res, jacobi_one(G, cond));
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}
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else if (nmod_mul(chi1->n, chi2->n, G->mod) == 1)
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{
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ulong n;
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n = jacobi_one(G, dirichlet_conductor_char(G, chi1));
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if (dirichlet_parity_char(G, chi1))
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acb_set_si(res, -n);
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else
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acb_set_si(res, n);
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}
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else
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{
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if (G->q <= 150)
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acb_dirichlet_jacobi_sum_naive(res, G, chi1, chi2, prec);
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else if (G->num > 1)
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acb_dirichlet_jacobi_sum_factor(res, G, chi1, chi2, prec);
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else if (G->P[0].e > 1)
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acb_dirichlet_jacobi_sum_naive(res, G, chi1, chi2, prec);
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else
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acb_dirichlet_jacobi_sum_gauss(res, G, chi1, chi2, prec);
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}
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}
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void
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acb_dirichlet_jacobi_sum_ui(acb_t res, const dirichlet_group_t G, ulong a, ulong b, slong prec)
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{
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if (G->q_even > 1)
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{
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acb_zero(res);
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}
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else if (a == 1 || b == 1)
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{
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ulong cond = (a == 1) ? dirichlet_conductor_ui(G, b) : dirichlet_conductor_ui(G, a);
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acb_set_si(res, jacobi_one(G, cond));
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}
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else if (nmod_mul(a, b, G->mod) == 1)
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{
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ulong n;
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n = jacobi_one(G, dirichlet_conductor_ui(G, a));
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if (dirichlet_parity_ui(G, a))
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acb_set_si(res, -n);
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else
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acb_set_si(res, n);
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}
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else
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{
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dirichlet_char_t chi1, chi2;
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dirichlet_char_init(chi1, G);
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dirichlet_char_init(chi2, G);
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dirichlet_char_log(chi1, G, a);
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dirichlet_char_log(chi2, G, b);
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acb_dirichlet_jacobi_sum(res, G, chi1, chi2, prec);
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dirichlet_char_clear(chi1);
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dirichlet_char_clear(chi2);
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}
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}
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