mirror of
https://github.com/vale981/arb
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79 lines
1.8 KiB
C
79 lines
1.8 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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#include "acb_poly.h"
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void
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acb_dirichlet_l_vec_hurwitz(acb_ptr res, const acb_t s,
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const acb_dirichlet_hurwitz_precomp_t precomp,
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const dirichlet_group_t G, slong prec)
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{
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acb_t a, qs;
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acb_ptr zeta, z;
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dirichlet_char_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 = acb_is_one(s);
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dirichlet_char_init(cn, G);
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acb_init(qs);
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acb_init(a);
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prec += n_clog(G->phi_q, 2);
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acb_set_ui(qs, G->q);
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acb_neg(a, s);
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acb_pow(qs, qs, a, prec);
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zeta = z = _acb_vec_init(G->phi_q);
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dirichlet_char_one(cn, G);
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do {
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if (precomp == NULL)
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{
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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(z, s, a, prec);
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else
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_acb_poly_zeta_cpx_series(z, s, a, 1, 1, prec);
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}
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else
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{
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acb_dirichlet_hurwitz_precomp_eval(z, precomp, cn->n, G->q, prec);
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}
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acb_mul(z, z, qs, prec);
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acb_conj(z, z);
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z++;
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} while (dirichlet_char_next(cn, G) >= 0);
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acb_dirichlet_dft_index(res, zeta, G, prec);
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{
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slong k;
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for (k = 0; k < G->phi_q; k++)
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acb_conj(res + k, res + k);
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}
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/* restore pole for the principal character */
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if (deflate)
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acb_indeterminate(res);
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dirichlet_char_clear(cn);
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_acb_vec_clear(zeta, G->phi_q);
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acb_clear(qs);
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acb_clear(a);
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}
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