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/*
Copyright (C) 2019 D.H.J Polymath
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"
static void
_arb_ui_pow_arb(arb_t res, ulong n, const arb_t x, slong prec)
{
arb_t a;
arb_init(a);
arb_set_ui(a, n);
arb_pow(res, a, x, prec);
arb_clear(a);
}
void
acb_dirichlet_platt_lemma_B1(arb_t out,
slong sigma, const arb_t t0, const arb_t h, slong J, slong prec)
{
arb_t pi, C;
arb_t x1, x2, x3;
if (sigma % 2 == 0 || sigma < 3)
{
arb_zero_pm_inf(out);
return;
}
arb_init(pi);
arb_init(C);
arb_init(x1);
arb_init(x2);
arb_init(x3);
arb_const_pi(pi, prec);
acb_dirichlet_platt_c_bound(C, sigma, t0, h, 0, prec);
arb_set_si(x1, 2*sigma - 1);
arb_div(x1, x1, h, prec);
arb_sqr(x1, x1, prec);
arb_mul_2exp_si(x1, x1, -3);
arb_exp(x1, x1, prec);
arb_set_si(x2, 1 - 2*sigma);
arb_mul_2exp_si(x2, x2, -2);
arb_pow(x2, pi, x2, prec);
arb_set_si(x3, 1 - sigma);
_arb_ui_pow_arb(x3, (ulong) J, x3, prec);
arb_div_si(x3, x3, sigma - 1, prec);
arb_mul(out, x1, x2, prec);
arb_mul(out, out, x3, prec);
arb_mul(out, out, C, prec);
arb_clear(pi);
arb_clear(C);
arb_clear(x1);
arb_clear(x2);
arb_clear(x3);
}
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