diff --git a/fmprb.h b/fmprb.h
index 85213a23..c6b5e7f2 100644
--- a/fmprb.h
+++ b/fmprb.h
@@ -192,6 +192,7 @@ void fmprb_const_zeta3_bsplit(fmprb_t x, long prec);
 void fmprb_zeta_ui_bsplit(fmprb_t x, ulong s, long prec);
 void fmprb_zeta_ui_euler_product(fmprb_t z, ulong s, long prec);
 void fmprb_zeta_ui_bernoulli(fmprb_t x, ulong n, long prec);
+void fmprb_zeta_ui(fmprb_t x, ulong n, long prec);
 
 static __inline__ void
 fmprb_add_error_2exp_si(fmprb_t x, long err)
diff --git a/fmprb/zeta_ui.c b/fmprb/zeta_ui.c
new file mode 100644
index 00000000..fcfb7191
--- /dev/null
+++ b/fmprb/zeta_ui.c
@@ -0,0 +1,74 @@
+/*=============================================================================
+
+    This file is part of ARB.
+
+    ARB is free software; you can redistribute it and/or modify
+    it under the terms of the GNU General Public License as published by
+    the Free Software Foundation; either version 2 of the License, or
+    (at your option) any later version.
+
+    ARB is distributed in the hope that it will be useful,
+    but WITHOUT ANY WARRANTY; without even the implied warranty of
+    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
+    GNU General Public License for more details.
+
+    You should have received a copy of the GNU General Public License
+    along with ARB; if not, write to the Free Software
+    Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA
+
+=============================================================================*/
+/******************************************************************************
+
+    Copyright (C) 2012 Fredrik Johansson
+
+******************************************************************************/
+
+#include <math.h>
+#include "arith.h"
+#include "fmprb.h"
+
+static void
+fmprb_zeta_ui_mpfr(fmprb_t x, ulong n, long prec)
+{
+    mpfr_t t;
+    mpfr_init2(t, prec);
+    mpfr_zeta_ui(t, n, MPFR_RNDD);
+    fmprb_zero(x);
+    fmpr_set_mpfr(fmprb_midref(x), t);
+    fmprb_add_error_2exp_si(x, mpfr_get_exp(t)-prec);
+    mpfr_clear(t);
+}
+
+void
+fmprb_zeta_ui(fmprb_t x, ulong n, long prec)
+{
+    /* asymptotic case */
+    if (n == 0 || n > 0.7 * prec)
+    {
+        fmprb_zeta_ui_mpfr(x, n, prec);
+    }
+    else if (n == 3)
+    {
+        fmprb_const_zeta3_bsplit(x, prec);
+    }
+    /* small even n */
+    else if ((n % 2 == 0) && (n < 40 + 0.11*prec))
+    {
+        fmprb_zeta_ui_bernoulli(x, n, prec);
+    }
+    /* small odd n, extremely high precision */
+    else if (n < prec * 0.0006)
+    {
+        fmprb_zeta_ui_bsplit(x, n, prec);
+    }
+    /* large n */
+    else if (prec > 20 && n > 0.4 * pow(prec, 0.8))
+    {
+        fmprb_zeta_ui_euler_product(x, n, prec);
+    }
+    /* fallback */
+    else
+    {
+        fmprb_zeta_ui_mpfr(x, n, prec);
+    }
+}