diff --git a/acb_dirichlet.h b/acb_dirichlet.h
index f2eca095..0a6e15e7 100644
--- a/acb_dirichlet.h
+++ b/acb_dirichlet.h
@@ -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
diff --git a/acb_dirichlet/riemann_xi.c b/acb_dirichlet/riemann_xi.c
new file mode 100644
index 00000000..de3e9245
--- /dev/null
+++ b/acb_dirichlet/riemann_xi.c
@@ -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);
+}
diff --git a/acb_dirichlet/test/t-riemann_xi.c b/acb_dirichlet/test/t-riemann_xi.c
new file mode 100644
index 00000000..da2a5fe1
--- /dev/null
+++ b/acb_dirichlet/test/t-riemann_xi.c
@@ -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;
+}