void
acb_dirichlet_l(acb_t res, const acb_t s,
const acb_dirichlet_group_t G, ulong m, slong prec)
{
acb_t chi, t, u, a;
ulong k;
acb_init(chi);
acb_init(t);
acb_init(u);
acb_init(a);
acb_zero(t);
for (k = 1; k <= G->q; k++)
{
acb_dirichlet_chi(chi, G, m, k, prec);
if (!acb_is_zero(chi))
{
acb_set_ui(a, k);
acb_div_ui(a, a, G->q, prec);
acb_hurwitz_zeta(u, s, a, prec);
acb_addmul(t, chi, u, prec);
}
}
acb_set_ui(u, G->q);
acb_neg(a, s);
acb_pow(u, u, a, prec);
acb_mul(res, t, u, prec);
acb_clear(chi);
acb_clear(t);
acb_clear(u);
acb_clear(a);
}
int main()
{
slong iter;
flint_rand_t state;
flint_printf("chi....");
fflush(stdout);
flint_randinit(state);
for (iter = 0; iter < 10000 * arb_test_multiplier(); iter++)
{
acb_t zn1, zn2, zn1n2, zn1zn2;
dirichlet_group_t G;
dirichlet_char_t chi;
ulong q, m, n1, n2, iter2;
int res;
q = 1 + n_randint(state, 1000);
dirichlet_group_init(G, q);
dirichlet_char_init(chi, G);
acb_init(zn1);
acb_init(zn2);
acb_init(zn1n2);
acb_init(zn1zn2);
/* check chi(n1) chi(n2) = chi(n1 n2) */
for (iter2 = 0; iter2 < 10; iter2++)
{
do {
m = 1 + n_randint(state, q);
} while (n_gcd(q, m) != 1);
dirichlet_char_log(chi, G, m);
n1 = n_randint(state, 1000);
n2 = n_randint(state, 1000);
acb_dirichlet_chi(zn1, G, chi, n1, 53);
acb_dirichlet_pairing(zn2, G, m, n1, 53);
if (!acb_overlaps(zn1, zn2))
{
flint_printf("FAIL: overlap\n\n");
flint_printf("q = %wu\n\n", q);
flint_printf("m = %wu\n\n", m);
flint_printf("n = %wu\n\n", n1);
flint_printf("char = "); acb_printd(zn1, 15); flint_printf("\n\n");
flint_printf("pairing = "); acb_printd(zn2, 15); flint_printf("\n\n");
dirichlet_char_print(G, chi);
dirichlet_char_log(chi, G, m);
flint_printf("log(m) = "); dirichlet_char_print(G, chi);
dirichlet_char_log(chi, G, n1);
flint_printf("log(n1) = "); dirichlet_char_print(G, chi);
flint_abort();
}
acb_dirichlet_pairing(zn2, G, m, n2, 53);
acb_dirichlet_pairing(zn1n2, G, m, n1 * n2, 53);
acb_mul(zn1zn2, zn1, zn2, 53);
if (!acb_overlaps(zn1n2, zn1zn2))
{
flint_printf("FAIL: overlap\n\n");
flint_printf("q = %wu\n\n", q);
flint_printf("m = %wu\n\n", m);
flint_printf("n1 = %wu\n\n", n1);
flint_printf("n2 = %wu\n\n", n2);
flint_printf("zn1 = "); acb_printd(zn1, 15); flint_printf("\n\n");
flint_printf("zn2 = "); acb_printd(zn2, 15); flint_printf("\n\n");
flint_printf("zn1n2 = "); acb_printd(zn1n2, 15); flint_printf("\n\n");
flint_printf("zn1zn2 = "); acb_printd(zn1zn2, 15); flint_printf("\n\n");
flint_abort();
}
}
if (iter % 10 == 0)
{
/* check orthogonality */
acb_zero(zn1);
n1 = n_randint(state, 1000);
for (m = 1; m <= q; m++)
{
if (n_gcd(q, m) == 1)
{
acb_dirichlet_pairing(zn2, G, m, n1, 53);
acb_add(zn1, zn1, zn2, 53);
}
}
if (n1 % q == 1 % q)
res = arb_contains_si(acb_realref(zn1), n_euler_phi(q)) &&
arb_contains_zero(acb_imagref(zn1));
else
res = acb_contains_zero(zn1);
if (!res)
{
flint_printf("FAIL: orthogonality\n\n");
flint_printf("q = %wu\n\n", q);
flint_printf("phi = %wu\n\n", n_euler_phi(q));
flint_printf("n1 = %wu\n\n", n1);
flint_printf("zn1 = "); acb_printd(zn1, 15); flint_printf("\n\n");
flint_abort();
}
}
dirichlet_group_clear(G);
dirichlet_char_clear(chi);
acb_clear(zn1);
acb_clear(zn2);
acb_clear(zn1n2);
acb_clear(zn1zn2);
}
flint_randclear(state);
flint_cleanup();
flint_printf("PASS\n");
return EXIT_SUCCESS;
}