mirror of
https://github.com/vale981/arb
synced 2025-03-05 09:21:38 -05:00
69 lines
1.7 KiB
C
69 lines
1.7 KiB
C
/*
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Copyright (C) 2018 D.H.J Polymath
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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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static void
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_acb_dirichlet_xi(acb_t res, const acb_t s, slong prec)
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{
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acb_t pi, z1, z2, z3;
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acb_init(pi);
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acb_init(z1);
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acb_init(z2);
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acb_init(z3);
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/* (s-1) * pi^(-s/2) * gamma(1 + s/2) * zeta(s) */
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acb_const_pi(pi, prec);
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acb_mul_2exp_si(z1, s, -1);
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acb_neg(z1, z1);
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acb_pow(z1, pi, z1, prec);
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acb_mul_2exp_si(z2, s, -1);
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acb_add_ui(z2, z2, 1, prec);
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acb_gamma(z2, z2, prec);
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acb_zeta(z3, s, prec);
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acb_sub_ui(res, s, 1, prec);
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acb_mul(res, res, z1, prec);
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acb_mul(res, res, z2, prec);
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acb_mul(res, res, z3, prec);
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acb_clear(pi);
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acb_clear(z1);
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acb_clear(z2);
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acb_clear(z3);
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}
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void acb_dirichlet_xi(acb_t res, const acb_t s, slong prec)
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{
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if (!acb_is_finite(s))
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{
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acb_indeterminate(res);
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}
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else if (acb_is_one(s))
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{
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acb_one(res);
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acb_mul_2exp_si(res, res, -1);
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}
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else if ((arf_sgn(arb_midref(acb_realref(s))) < 0 &&
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!acb_contains_zero(s)) ||
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(arb_contains_si(acb_realref(s), 1) && /* also intervals around s = 1 */
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arb_contains_zero(acb_imagref(s))))
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{
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acb_sub_ui(res, s, 1, prec);
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acb_neg(res, res);
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_acb_dirichlet_xi(res, res, prec);
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}
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else
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{
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_acb_dirichlet_xi(res, s, prec);
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}
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}
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