mirror of
https://github.com/vale981/arb
synced 2025-03-05 09:21:38 -05:00
6bf072eb59
This will allow us to not loose the julia session on error. See also https://github.com/wbhart/flint2/pull/243
126 lines
3 KiB
C
126 lines
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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#include "acb_poly.h"
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void
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acb_dirichlet_hardy_theta(acb_ptr res, const acb_t t,
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const dirichlet_group_t G, const dirichlet_char_t chi,
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slong len, slong prec)
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{
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acb_struct y[2];
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arb_t c;
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slong k;
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int parity;
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ulong q;
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if (len <= 0)
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return;
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if (t == res)
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{
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acb_init(y);
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acb_set(y, t);
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acb_dirichlet_hardy_theta(res, y, G, chi, len, prec);
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acb_clear(y);
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return;
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}
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if (G == NULL)
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{
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parity = 0;
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q = 1;
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}
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else
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{
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parity = dirichlet_parity_char(G, chi);
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q = G->q;
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if (q != dirichlet_conductor_char(G, chi))
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{
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flint_printf("hardy theta: need primitive character\n");
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flint_abort();
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}
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}
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if (!acb_is_finite(t))
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{
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_acb_vec_indeterminate(res, len);
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return;
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}
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acb_init(y + 0);
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acb_init(y + 1);
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arb_init(c);
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/* res = log gamma((s+parity)/2), s = 0.5+i(t+x) */
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acb_mul_onei(y, t);
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arb_set_d(c, 0.5 + parity);
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arb_add(acb_realref(y), acb_realref(y), c, prec);
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acb_mul_2exp_si(y, y, -1);
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acb_onei(y + 1);
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acb_mul_2exp_si(y + 1, y + 1, -1);
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_acb_poly_lgamma_series(res, y, FLINT_MIN(len, 2), len, prec);
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if (acb_is_real(t))
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{
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for (k = 0; k < len; k++)
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{
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arb_set(acb_realref(res + k), acb_imagref(res + k));
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arb_zero(acb_imagref(res + k));
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}
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}
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else
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{
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acb_ptr v = _acb_vec_init(len);
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/* v = log gamma(((1-s)+parity)/2), s = 0.5+i(t+x) */
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acb_div_onei(y, t);
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arb_set_d(c, 0.5 + parity);
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arb_add(acb_realref(y), acb_realref(y), c, prec);
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acb_mul_2exp_si(y, y, -1);
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acb_neg(y + 1, y + 1);
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_acb_poly_lgamma_series(v, y, FLINT_MIN(len, 2), len, prec);
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_acb_vec_sub(res, res, v, len, prec);
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for (k = 0; k < len; k++)
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{
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acb_div_onei(res + k, res + k);
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acb_mul_2exp_si(res + k, res + k, -1);
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}
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_acb_vec_clear(v, len);
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}
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/* (t+x) [-(1/2) log(pi/q)] */
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arb_const_pi(c, prec);
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arb_div_ui(c, c, q, prec);
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arb_log(c, c, prec);
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arb_mul_2exp_si(c, c, -1);
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acb_submul_arb(res, t, c, prec);
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if (len > 1)
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acb_sub_arb(res + 1, res + 1, c, prec);
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/* i log(eps) / 2 */
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if (q > 1)
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{
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acb_dirichlet_root_number(y, G, chi, prec);
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acb_arg(c, y, prec);
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arb_mul_2exp_si(c, c, -1);
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arb_sub(acb_realref(res), acb_realref(res), c, prec);
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}
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acb_clear(y + 0);
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acb_clear(y + 1);
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arb_clear(c);
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}
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