diff --git a/acb_dirichlet/dft_convol_fft.c b/acb_dirichlet/dft_convol_fft.c
new file mode 100644
index 00000000..23a3b72d
--- /dev/null
+++ b/acb_dirichlet/dft_convol_fft.c
@@ -0,0 +1,58 @@
+/*
+    Copyright (C) 2016 Pascal Molin
+
+    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"
+
+/* assume np >= 2 * n - 1 */
+void
+acb_dirichlet_dft_convol_pad(acb_ptr fp, acb_ptr gp, acb_srcptr f, acb_srcptr g, slong n, slong np)
+{
+    slong k;
+    for (k = 0; k < n; k++)
+        acb_set(gp + k, g + k);
+    for (k = 0; k < n; k++)
+        acb_set(fp + k, f + k);
+    for (k = 1; k < n; k++)
+        acb_set(fp + np - k, f + n - k);
+    for (k = n; k <= np - n; k++)
+        acb_zero(fp + k);
+}
+
+void
+acb_dirichlet_dft_inverse_cyc(acb_ptr w, acb_srcptr v, slong len, slong prec)
+{
+    /* divide before to keep v const */
+    _acb_vec_scalar_div_ui(w, v, len, len, prec);
+    acb_vec_swap_ri(w, len);
+    acb_dirichlet_dft_cyc(w, w, len, prec);
+    acb_vec_swap_ri(w, len);
+}
+
+void
+acb_dirichlet_dft_convol_fft(acb_ptr w, acb_srcptr f, acb_srcptr g, slong len, slong prec)
+{
+    int e;
+    slong k, np;
+    acb_ptr fp, gp;
+    acb_dirichlet_dft_rad2_t dft;
+    e = n_clog(2 * len + 1, 2);
+    acb_dirichlet_dft_rad2_init(dft, e, prec);
+    np = dft->n;
+    fp = _acb_vec_init(np);
+    gp = _acb_vec_init(np);
+    acb_dirichlet_dft_convol_pad(fp, gp, f, g, len, np);
+    acb_dirichlet_dft_rad2_precomp(fp, dft, prec);
+    acb_dirichlet_dft_rad2_precomp(gp, dft, prec);
+    _acb_vec_kronecker_mul(gp, gp, fp, np, prec);
+    acb_dirichlet_dft_inverse_rad2_precomp(gp, dft, prec);
+    for (k = 0; k < len; k++)
+        acb_set(w + k, gp + k);
+}
diff --git a/acb_dirichlet/dft_convol_naive.c b/acb_dirichlet/dft_convol_naive.c
new file mode 100644
index 00000000..be7f2c8e
--- /dev/null
+++ b/acb_dirichlet/dft_convol_naive.c
@@ -0,0 +1,31 @@
+/*
+    Copyright (C) 2016 Pascal Molin
+
+    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_dirichlet_dft_convol_naive(acb_ptr w, acb_srcptr f, acb_srcptr g, slong len, slong prec)
+{
+    slong x, y;
+    for (x = 0; x < len; x ++)
+    {
+        acb_ptr wx;
+        acb_srcptr fx, gy;
+        wx = w + x;
+        fx = f + x;
+        gy = g;
+        acb_zero(wx);
+        for (y = 0; y <= x; y++)
+            acb_addmul(wx, fx--, gy++, prec);
+        for (; y < len; y++)
+            acb_addmul(wx, f + x - y, g + y, prec);
+    }
+}