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add riemann xi function

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p15-git-acct 2018-03-28 21:19:51 -05:00
parent e074eeaec6
commit 70af397ab4
3 changed files with 127 additions and 0 deletions
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2
acb_dirichlet.h
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@ -45,6 +45,8 @@ void acb_dirichlet_zeta(acb_t res, const acb_t s, slong prec);
void acb_dirichlet_zeta_jet_rs(acb_ptr res, const acb_t s, slong len, slong prec);
void acb_dirichlet_zeta_jet(acb_t res, const acb_t s, int deflate, slong len, slong prec);
void acb_riemann_xi(acb_t res, const acb_t s, slong prec);
void acb_dirichlet_hurwitz(acb_t res, const acb_t s, const acb_t a, slong prec);
typedef struct

51
acb_dirichlet/riemann_xi.c Normal file
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@ -0,0 +1,51 @@
/*
Copyright (C) 2018 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"
void acb_riemann_xi(acb_t res, const acb_t s, slong prec)
{
acb_t pi, z1, z2, z3, z4;
acb_init(pi);
acb_const_pi(pi, prec);
/* s*(s-1)/2 */
acb_init(z1);
acb_sub_ui(z1, s, 1, prec);
acb_mul(z1, z1, s, prec);
acb_mul_2exp_si(z1, z1, -1);
/* pi^(-s/2) */
acb_init(z2);
acb_mul_2exp_si(z2, s, -1);
acb_neg(z2, z2);
acb_pow(z2, pi, z2, prec);
/* gamma(s/2) */
acb_init(z3);
acb_mul_2exp_si(z3, s, -1);
acb_gamma(z3, z3, prec);
/* zeta(s) */
acb_init(z4);
acb_zeta(z4, s, prec);
acb_mul(res, z1, z2, prec);
acb_mul(res, res, z3, prec);
acb_mul(res, res, z4, prec);
acb_clear(pi);
acb_clear(z1);
acb_clear(z2);
acb_clear(z3);
acb_clear(z4);
}

74
acb_dirichlet/test/t-riemann_xi.c Normal file
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@ -0,0 +1,74 @@
/*
Copyright (C) 2018 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"
int main()
{
slong iter;
flint_rand_t state;
flint_printf("riemann_xi....");
fflush(stdout);
flint_randinit(state);
for (iter = 0; iter < 3000 * arb_test_multiplier(); iter++)
{
acb_t a, b, c;
slong prec1, prec2;
prec1 = 2 + n_randint(state, 1000);
prec2 = prec1 + 30;
acb_init(a);
acb_init(b);
acb_init(c);
arb_randtest_precise(acb_realref(a), state, 1 + n_randint(state, 1000), 3);
arb_randtest_precise(acb_imagref(a), state, 1 + n_randint(state, 1000), 3);
acb_riemann_xi(b, a, prec1);
acb_riemann_xi(c, a, prec2);
if (!acb_overlaps(b, c))
{
flint_printf("FAIL: overlap\n\n");
flint_printf("a = "); acb_print(a); flint_printf("\n\n");
flint_printf("b = "); acb_print(b); flint_printf("\n\n");
flint_printf("c = "); acb_print(c); flint_printf("\n\n");
flint_abort();
}
/* check riemann_xi(s) = riemann_xi(1-s) */
acb_sub_ui(c, a, 1, prec1);
acb_neg(c, c);
acb_riemann_xi(c, c, prec1);
if (!acb_overlaps(b, c))
{
flint_printf("FAIL: functional equation\n\n");
flint_printf("a = "); acb_print(a); flint_printf("\n\n");
flint_printf("b = "); acb_print(b); flint_printf("\n\n");
flint_printf("c = "); acb_print(c); flint_printf("\n\n");
flint_abort();
}
acb_clear(a);
acb_clear(b);
acb_clear(c);
}
flint_randclear(state);
flint_cleanup();
flint_printf("PASS\n");
return EXIT_SUCCESS;
}