mirror of
https://github.com/vale981/arb
synced 2025-03-06 09:51:39 -05:00
143 lines
4.3 KiB
C
143 lines
4.3 KiB
C
/*=============================================================================
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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
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it under the terms of the GNU General Public License as published by
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the Free Software Foundation; either version 2 of the License, or
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(at your option) any later version.
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ARB is distributed in the hope that it will be useful,
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but WITHOUT ANY WARRANTY; without even the implied warranty of
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MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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GNU General Public License for more details.
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You should have received a copy of the GNU General Public License
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along with ARB; if not, write to the Free Software
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Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA
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=============================================================================*/
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/******************************************************************************
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Copyright (C) 2016 Pascal Molin
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******************************************************************************/
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#include "acb_dirichlet.h"
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int main()
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{
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slong prec = 64;
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ulong q;
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flint_printf("thetanull....");
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fflush(stdout);
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/* check the only theta functions
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* theta(chi) = sum chi(k)* k^odd * exp(-Pi * k^2 / q)
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* vanishing at 1 correspond to two specific
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* characters of moduli 300 and 600 + conjugates
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*/
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for (q = 3; q < 1000; q ++)
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{
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acb_dirichlet_group_t G;
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acb_dirichlet_conrey_t x;
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acb_dirichlet_char_t chi;
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ulong * v, nv, k;
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acb_t zeta, sum;
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acb_ptr z;
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arb_t eq;
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arb_ptr t, kt, tt;
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if (q % 4 == 2)
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/* no primitive character mod q */
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continue;
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acb_dirichlet_group_init(G, q);
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acb_dirichlet_conrey_init(x, G);
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acb_dirichlet_char_init(chi, G);
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acb_init(zeta);
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acb_dirichlet_nth_root(zeta, G->expo, prec);
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z = _acb_vec_init(G->expo);
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_acb_vec_set_powers(z, zeta, G->expo, prec);
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nv = acb_dirichlet_theta_length_d(q, 1, prec);
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v = flint_malloc(nv * sizeof(ulong));
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arb_init(eq);
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arb_const_pi(eq, prec);
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arb_div_ui(eq, eq, q, prec);
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arb_neg(eq, eq);
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arb_exp(eq, eq, prec);
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t = _arb_vec_init(nv);
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acb_dirichlet_arb_quadratic_powers(t, nv, eq, prec);
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kt = _arb_vec_init(nv);
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for (k = 1; k < nv; k++)
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arb_mul_ui(kt + k, t + k, k, prec);
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/* theta function on primitive characters */
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acb_init(sum);
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acb_dirichlet_conrey_first_primitive(x, G);
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while (1) {
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ulong m;
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acb_zero(sum);
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acb_dirichlet_char_conrey(chi, G, x);
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acb_dirichlet_ui_chi_vec(v, G, chi, nv);
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m = G->expo / chi->order;
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tt = acb_dirichlet_char_parity(chi) ? kt : t;
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for (k = 1; k < nv; k++)
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if (v[k] != ACB_DIRICHLET_CHI_NULL)
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acb_addmul_arb(sum, z + (v[k] * m), tt + k, prec);
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if ((q == 300 && (chi->x->n == 271 || chi->x->n == 131))
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|| (q == 600 && (chi->x->n == 11 || chi->x->n == 91)))
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{
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if (!acb_contains_zero(sum))
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{
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flint_printf("FAIL: Theta(chi_%wu(%wu))=", q, chi->x->n);
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acb_printd(sum, 10);
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flint_printf("\n");
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acb_dirichlet_char_print(G, chi);
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flint_printf("\n");
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abort();
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}
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}
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else if (acb_contains_zero(sum))
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{
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flint_printf("FAIL: Theta(chi_%wu(%wu))=", q, chi->x->n);
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acb_printd(sum, 10);
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flint_printf("\n");
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acb_dirichlet_char_print(G, chi);
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flint_printf("\n");
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abort();
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}
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if (acb_dirichlet_conrey_next_primitive(x, G) == G->num)
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break;
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}
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_acb_vec_clear(z, G->expo);
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_arb_vec_clear(t, nv);
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acb_clear(zeta);
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acb_clear(sum);
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arb_clear(eq);
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flint_free(v);
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acb_dirichlet_group_clear(G);
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acb_dirichlet_char_clear(chi);
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acb_dirichlet_conrey_clear(x);
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}
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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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