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/*
Copyright (C) 2016 Fredrik Johansson
This file is part of Arb.
Arb is free software: you can redistribute it and/or modify it under
the terms of the GNU Lesser General Public License (LGPL) as published
by the Free Software Foundation; either version 2.1 of the License, or
(at your option) any later version. See <http://www.gnu.org/licenses/>.
*/
#include "acb_dirichlet.h"
#include "acb_poly.h"
void
acb_dirichlet_hurwitz_precomp_eval(acb_t res,
const acb_dirichlet_hurwitz_precomp_t pre, ulong p, ulong q, slong prec)
{
slong i;
acb_t a, t;
if (p > q)
{
flint_printf("hurwitz_precomp_eval: require p <= n\n");
flint_abort();
}
if (pre->A == 0)
{
acb_init(a);
acb_set_ui(a, p);
acb_div_ui(a, a, q, prec);
if (pre->deflate == 0)
acb_hurwitz_zeta(res, &pre->s, a, prec);
else
_acb_poly_zeta_cpx_series(res, &pre->s, a, 1, 1, prec);
acb_clear(a);
return;
}
acb_init(a);
acb_init(t);
/* todo: avoid integer overflows below */
if (p == q)
i = pre->N - 1;
else
i = (pre->N * p) / q;
acb_set_si(a, 2 * pre->N * p - q * (2 * i + 1));
acb_div_ui(a, a, 2 * q * pre->N, prec);
/* compute zeta(s,A+p/q) */
_acb_poly_evaluate(res, pre->coeffs + i * pre->K, pre->K, a, prec);
/* error bound */
if (acb_is_real(&pre->s))
arb_add_error_mag(acb_realref(res), &pre->err);
else
acb_add_error_mag(res, &pre->err);
/* zeta(s,p/q) = (p/q)^-s + ... + (p/q+A-1)^-s zeta(s,A+p/q) */
for (i = 0; i < pre->A; i++)
{
acb_set_ui(a, p);
acb_div_ui(a, a, q, prec);
acb_add_ui(a, a, i, prec);
acb_neg(t, &pre->s);
acb_pow(a, a, t, prec);
acb_add(res, res, a, prec);
}
acb_clear(a);
acb_clear(t);
}
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