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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_div_ui_ui(arb_t res, ulong a, ulong b, slong prec)
{
arb_set_ui(res, a);
arb_div_ui(res, res, b, prec);
}
static int
_arb_lt_d(const arb_t a, double d)
{
int result;
arb_t x;
arb_init(x);
arb_set_d(x, d);
result = arb_lt(a, x);
arb_clear(x);
return result;
}
int main()
{
slong iter;
flint_rand_t state;
arb_t x, t, t0, expe;
flint_printf("platt_beta....");
fflush(stdout);
flint_randinit(state);
arb_init(x);
arb_init(t);
arb_init(t0);
arb_init(expe);
for (iter = 0; iter < 10000 * arb_test_multiplier(); iter++)
{
arb_t beta, a, b, c;
acb_t z;
slong prec, mbits;
prec = 2 + n_randint(state, 300);
mbits = 2 + n_randint(state, 20);
arb_randtest(t, state, prec, mbits);
arb_randtest(t0, state, prec, mbits);
arb_abs(t, t);
arb_abs(t0, t0);
arb_add(x, t, t0, prec);
arb_const_e(expe, prec);
arb_exp(expe, expe, prec);
if (!arb_is_nonnegative(t) || !arb_gt(t0, expe) || !_arb_lt_d(x, 1e8))
{
continue;
}
arb_init(beta);
arb_init(a);
arb_init(b);
arb_init(c);
acb_init(z);
acb_dirichlet_platt_beta(beta, t0, prec);
/* Lemma A.10 in "Isolating some non-trivial zeros of zeta" */
arb_pow(a, x, beta, prec);
arb_mul_ui(a, a, 3, prec);
acb_dirichlet_platt_scaled_lambda(c, t, prec);
arb_abs(c, c);
if (arb_gt(c, a))
{
flint_printf("FAIL: Lemma A.10 |f(t)|\n\n");
flint_printf("iter = %wd\n\n", iter);
flint_printf("prec = %wd\n\n", prec);
flint_printf("t = "); arb_printd(t, 15); flint_printf("\n\n");
flint_printf("t0 = "); arb_printd(t0, 15); flint_printf("\n\n");
flint_abort();
}
/* In Lemma A.10 proof in "Isolating some non-trivial zeros of zeta" */
arb_pow(a, x, beta, prec);
_arb_div_ui_ui(b, 732, 1000, prec);
arb_mul(a, a, b, prec);
acb_set_d(z, 0.5);
arb_set(acb_imagref(z), x);
acb_zeta(z, z, prec);
acb_abs(c, z, prec);
if (arb_gt(c, a))
{
flint_printf("FAIL: Lemma A.10 |zeta(1/2 + i(t + t0))|\n\n");
flint_printf("iter = %wd\n\n", iter);
flint_printf("prec = %wd\n\n", prec);
flint_printf("t = "); arb_printd(t, 15); flint_printf("\n\n");
flint_printf("t0 = "); arb_printd(t0, 15); flint_printf("\n\n");
flint_abort();
}
arb_clear(beta);
arb_clear(a);
arb_clear(b);
arb_clear(c);
acb_clear(z);
}
arb_clear(x);
arb_clear(t);
arb_clear(t0);
arb_clear(expe);
flint_randclear(state);
flint_cleanup();
flint_printf("PASS\n");
return EXIT_SUCCESS;
}
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