mirror of
https://github.com/vale981/arb
synced 2025-03-04 17:01:40 -05:00
126 lines
3.2 KiB
C
126 lines
3.2 KiB
C
/*
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Copyright (C) 2019 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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_arb_div_ui_ui(arb_t res, ulong a, ulong b, slong prec)
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{
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arb_set_ui(res, a);
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arb_div_ui(res, res, b, prec);
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}
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static int
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_arb_lt_d(const arb_t a, double d)
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{
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int result;
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arb_t x;
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arb_init(x);
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arb_set_d(x, d);
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result = arb_lt(a, x);
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arb_clear(x);
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return result;
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}
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int main()
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{
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slong iter;
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flint_rand_t state;
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arb_t x, t, t0, expe;
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flint_printf("platt_beta....");
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fflush(stdout);
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flint_randinit(state);
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arb_init(x);
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arb_init(t);
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arb_init(t0);
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arb_init(expe);
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for (iter = 0; iter < 10000 * arb_test_multiplier(); iter++)
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{
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arb_t beta, a, b, c;
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acb_t z;
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slong prec, mbits;
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prec = 2 + n_randint(state, 300);
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mbits = 2 + n_randint(state, 20);
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arb_randtest(t, state, prec, mbits);
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arb_randtest(t0, state, prec, mbits);
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arb_abs(t, t);
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arb_abs(t0, t0);
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arb_add(x, t, t0, prec);
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arb_const_e(expe, prec);
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arb_exp(expe, expe, prec);
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if (!arb_is_nonnegative(t) || !arb_gt(t0, expe) || !_arb_lt_d(x, 1e8))
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{
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continue;
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}
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arb_init(beta);
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arb_init(a);
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arb_init(b);
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arb_init(c);
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acb_init(z);
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acb_dirichlet_platt_beta(beta, t0, prec);
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/* Lemma A.10 in "Isolating some non-trivial zeros of zeta" */
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arb_pow(a, x, beta, prec);
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arb_mul_ui(a, a, 3, prec);
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acb_dirichlet_platt_scaled_lambda(c, t, prec);
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arb_abs(c, c);
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if (arb_gt(c, a))
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{
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flint_printf("FAIL: Lemma A.10 |f(t)|\n\n");
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flint_printf("iter = %wd\n\n", iter);
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flint_printf("prec = %wd\n\n", prec);
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flint_printf("t = "); arb_printd(t, 15); flint_printf("\n\n");
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flint_printf("t0 = "); arb_printd(t0, 15); flint_printf("\n\n");
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flint_abort();
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}
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/* In Lemma A.10 proof in "Isolating some non-trivial zeros of zeta" */
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arb_pow(a, x, beta, prec);
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_arb_div_ui_ui(b, 732, 1000, prec);
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arb_mul(a, a, b, prec);
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acb_set_d(z, 0.5);
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arb_set(acb_imagref(z), x);
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acb_zeta(z, z, prec);
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acb_abs(c, z, prec);
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if (arb_gt(c, a))
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{
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flint_printf("FAIL: Lemma A.10 |zeta(1/2 + i(t + t0))|\n\n");
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flint_printf("iter = %wd\n\n", iter);
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flint_printf("prec = %wd\n\n", prec);
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flint_printf("t = "); arb_printd(t, 15); flint_printf("\n\n");
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flint_printf("t0 = "); arb_printd(t0, 15); flint_printf("\n\n");
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flint_abort();
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}
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arb_clear(beta);
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arb_clear(a);
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arb_clear(b);
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arb_clear(c);
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acb_clear(z);
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}
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arb_clear(x);
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arb_clear(t);
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arb_clear(t0);
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arb_clear(expe);
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flint_randclear(state);
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flint_cleanup();
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flint_printf("PASS\n");
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return EXIT_SUCCESS;
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}
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