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https://github.com/vale981/arb
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46fa645910
- try to handle even and odd components the same way in the dirichlet group - switch from phi_q_odd to smaller expo = exponent of the group all character orders divide this number, and a character of that order exists - use conrey logarithm to reuse log and to loop efficiently over the group (see the diff on l.c, only 1 log in computed instead of 2 * q) - NOT TESTED, for the moment it just compiles, I know some errors (e.g. the FIXME in group_init.c : the generators have to be lifted mod q) this commit is just a proof of concept.
58 lines
1.3 KiB
C
58 lines
1.3 KiB
C
/*
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Copyright (C) 2016 Fredrik Johansson
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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_l(acb_t res, const acb_t s,
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const acb_dirichlet_group_t G, ulong m, slong prec)
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{
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acb_t chi, t, u, a;
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acb_conrey_t cm, cn;
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acb_init(chi);
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acb_conrey_init(cm, G);
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acb_conrey_init(cn, G);
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acb_init(t);
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acb_init(u);
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acb_init(a);
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acb_conrey_log(cm, G, m);
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acb_conrey_one(cn, G);
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acb_zero(t);
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while (1) {
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/* todo: use n_dirichlet_chi and precomputed roots instead */
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acb_dirichlet_chi_conrey(chi, G, cm, cn, prec);
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acb_set_ui(a, cn->n);
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acb_div_ui(a, a, G->q, prec);
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acb_hurwitz_zeta(u, s, a, prec);
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acb_addmul(t, chi, u, prec);
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if (acb_conrey_next(cn, G) == G->num)
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break;
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}
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acb_set_ui(u, G->q);
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acb_neg(a, s);
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acb_pow(u, u, a, prec);
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acb_mul(res, t, u, prec);
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acb_conrey_clear(cm);
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acb_conrey_clear(cn);
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acb_clear(chi);
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acb_clear(t);
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acb_clear(u);
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acb_clear(a);
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}
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