mirror of
https://github.com/vale981/arb
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80 lines
1.9 KiB
C
80 lines
1.9 KiB
C
/*
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Copyright (C) 2016 Fredrik Johansson
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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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#include "acb_poly.h"
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/* todo: should document or fix that it doesn't allow aliasing */
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void
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acb_dirichlet_l_hurwitz(acb_t res, const acb_t s,
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const acb_dirichlet_group_t G, const acb_dirichlet_char_t chi, slong prec)
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{
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ulong chin;
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acb_t t, u, a;
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acb_ptr z;
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acb_dirichlet_conrey_t cn;
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int deflate;
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/* remove pole in Hurwitz zeta at s = 1 */
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deflate = 0;
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if (acb_is_one(s))
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{
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/* character is principal */
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if (chi->x->n == 1)
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{
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acb_indeterminate(res);
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return;
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}
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deflate = 1;
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}
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acb_dirichlet_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_dirichlet_conrey_one(cn, G);
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acb_zero(t);
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prec += n_clog(G->phi_q, 2);
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z = _acb_vec_init(chi->order.n);
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acb_dirichlet_vec_nth_roots(z, chi->order.n, prec);
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do {
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chin = acb_dirichlet_ui_chi_conrey(G, chi, cn);
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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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if (deflate == 0)
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acb_hurwitz_zeta(u, s, a, prec);
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else
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_acb_poly_zeta_cpx_series(u, s, a, 1, 1, prec);
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acb_addmul(t, z + chin, u, prec);
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} while (acb_dirichlet_conrey_next(cn, G) >= 0);
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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_dirichlet_conrey_clear(cn);
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_acb_vec_clear(z, chi->order.n);
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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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