int main() { slong iter; flint_rand_t state; flint_printf("hardy_z_series...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 200 * arb_test_multiplier(); iter++) { slong m, n1, n2, bits1, bits2, bits3; acb_poly_t S, A, B, C; dirichlet_group_t G; dirichlet_char_t chi; ulong q; bits1 = 2 + n_randint(state, 200); bits2 = 2 + n_randint(state, 200); bits3 = 2 + n_randint(state, 200); m = 1 + n_randint(state, 8); n1 = 1 + n_randint(state, 8); n2 = 1 + n_randint(state, 8); do { q = 1 + n_randint(state, 15); } while (q % 4 == 2); dirichlet_group_init(G, q); dirichlet_char_init(chi, G); do { dirichlet_char_index(chi, G, n_randint(state, G->phi_q)); } while (!dirichlet_char_is_primitive(G, chi)); acb_poly_init(S); acb_poly_init(A); acb_poly_init(B); acb_poly_init(C); acb_poly_randtest(S, state, m, bits1, 3); acb_dirichlet_hardy_z_series(A, S, G, chi, n1, bits2); acb_poly_set(B, S); /* aliasing */ if (q == 1 && n_randint(state, 2)) acb_poly_neg(B, B); acb_dirichlet_hardy_z_series(B, B, G, chi, n2, bits3); acb_poly_set(C, A); acb_poly_truncate(C, FLINT_MIN(n1, n2)); acb_poly_truncate(B, FLINT_MIN(n1, n2)); if (!acb_poly_overlaps(B, C)) { flint_printf("FAIL\n\n"); flint_printf("S = "); acb_poly_printd(S, 15); flint_printf("\n\n"); flint_printf("A = "); acb_poly_printd(A, 15); flint_printf("\n\n"); flint_printf("B = "); acb_poly_printd(B, 15); flint_printf("\n\n"); abort(); } acb_poly_clear(S); acb_poly_clear(A); acb_poly_clear(B); acb_poly_clear(C); dirichlet_char_clear(chi); dirichlet_group_clear(G); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; }
void acb_dirichlet_l(acb_t res, const acb_t s, const dirichlet_group_t G, const dirichlet_char_t chi, slong prec) { if (!acb_is_finite(s)) { acb_indeterminate(res); } else if (G == NULL || G->q == 1) { acb_dirichlet_zeta(res, s, prec); } else if (dirichlet_char_is_primitive(G, chi) && (arf_cmp_d(arb_midref(acb_realref(s)), -0.5) < 0 || (G->q != 1 && dirichlet_parity_char(G, chi) == 0 && arf_cmpabs_d(arb_midref(acb_imagref(s)), 0.125) < 0 && arf_cmp_d(arb_midref(acb_realref(s)), 0.125) < 0))) { /* use functional equation */ acb_t t, u, v; int parity; ulong q; parity = dirichlet_parity_char(G, chi); q = G->q; acb_init(t); acb_init(u); acb_init(v); /* gamma((1-s+p)/2) / gamma((s+p)/2) */ acb_add_ui(t, s, parity, prec); acb_mul_2exp_si(t, t, -1); acb_rgamma(t, t, prec); if (!acb_is_zero(t)) /* assumes q != 1 when s = 0 */ { acb_neg(u, s); acb_add_ui(u, u, 1 + parity, prec); acb_mul_2exp_si(u, u, -1); acb_gamma(u, u, prec); acb_mul(t, t, u, prec); /* epsilon */ acb_dirichlet_root_number(u, G, chi, prec); acb_mul(t, t, u, prec); /* (pi/q)^(s-1/2) */ acb_const_pi(u, prec); acb_div_ui(u, u, q, prec); acb_set_d(v, -0.5); acb_add(v, v, s, prec); acb_pow(u, u, v, prec); acb_mul(t, t, u, prec); acb_sub_ui(u, s, 1, prec); acb_neg(u, u); acb_conj(u, u); acb_dirichlet_l_general(u, u, G, chi, prec); acb_conj(u, u); acb_mul(t, t, u, prec); if (dirichlet_char_is_real(G, chi) && acb_is_real(s)) arb_zero(acb_imagref(t)); } acb_set(res, t); acb_clear(t); acb_clear(u); acb_clear(v); } else { acb_dirichlet_l_general(res, s, G, chi, prec); } }