mirror of
https://github.com/vale981/arb
synced 2025-03-06 09:51:39 -05:00
100 lines
2.2 KiB
C
100 lines
2.2 KiB
C
/*
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Copyright (C) 2012 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.h"
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#include "acb_poly.h"
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void
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acb_zeta_si(acb_t z, slong s, slong prec)
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{
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if (s >= 0)
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{
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arb_zeta_ui(acb_realref(z), s, prec);
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}
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else
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{
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arb_bernoulli_ui(acb_realref(z), 1-s, prec);
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arb_div_ui(acb_realref(z), acb_realref(z), 1-s, prec);
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arb_neg(acb_realref(z), acb_realref(z));
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}
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arb_zero(acb_imagref(z));
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return;
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}
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void
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acb_hurwitz_zeta(acb_t z, const acb_t s, const acb_t a, slong prec)
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{
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if (acb_is_one(a) && acb_is_int(s) &&
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arf_cmpabs_2exp_si(arb_midref(acb_realref(s)), FLINT_BITS - 1) < 0)
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{
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acb_zeta_si(z, arf_get_si(arb_midref(acb_realref(s)), ARF_RND_DOWN), prec);
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return;
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}
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_acb_poly_zeta_cpx_series(z, s, a, 0, 1, prec);
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}
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void
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acb_zeta(acb_t z, const acb_t s, slong prec)
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{
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acb_t a;
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acb_init(a);
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acb_one(a);
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if (acb_is_int(s) &&
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arf_cmpabs_2exp_si(arb_midref(acb_realref(s)), FLINT_BITS - 1) < 0)
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{
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acb_zeta_si(z, arf_get_si(arb_midref(acb_realref(s)), ARF_RND_DOWN), prec);
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return;
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}
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if (arf_sgn(arb_midref(acb_realref(s))) < 0)
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{
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acb_t t, u, v;
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slong wp = prec + 6;
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acb_init(t);
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acb_init(u);
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acb_init(v);
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acb_sub_ui(t, s, 1, wp);
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/* 2 * (2pi)^(s-1) */
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arb_const_pi(acb_realref(u), wp);
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acb_mul_2exp_si(u, u, 1);
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acb_pow(u, u, t, wp);
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acb_mul_2exp_si(u, u, 1);
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/* sin(pi*s/2) */
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acb_mul_2exp_si(v, s, -1);
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acb_sin_pi(v, v, wp);
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acb_mul(u, u, v, wp);
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/* gamma(1-s) zeta(1-s) */
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acb_neg(t, t);
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acb_gamma(v, t, wp);
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acb_mul(u, u, v, wp);
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acb_hurwitz_zeta(v, t, a, wp);
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acb_mul(z, u, v, prec);
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acb_clear(t);
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acb_clear(u);
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acb_clear(v);
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}
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else
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{
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acb_hurwitz_zeta(z, s, a, prec);
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}
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acb_clear(a);
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}
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