From 224a3ded41270fac30caaee3251c16552ca81245 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Fr=C3=A9d=C3=A9ric=20Chapoton?= <chapoton@unistra.fr>
Date: Mon, 29 Jan 2024 19:14:53 +0100
Subject: [PATCH] add lfunction to hypergeometric motives

---
 src/sage/lfunctions/pari.py               | 22 +++++++++++++++++++++
 src/sage/modular/hypergeometric_motive.py | 24 +++++++++++++++++++++++
 2 files changed, 46 insertions(+)

diff --git a/src/sage/lfunctions/pari.py b/src/sage/lfunctions/pari.py
index e4968866303..694f3ad123e 100644
--- a/src/sage/lfunctions/pari.py
+++ b/src/sage/lfunctions/pari.py
@@ -256,6 +256,28 @@ def lfun_character(chi):
     return pari.lfuncreate([G, v])
 
 
+def lfun_hgm(motif, t):
+    """
+    Create the L-function of an hypergeometric motive.
+
+    OUTPUT:
+
+    one :pari:`lfun` object
+
+    EXAMPLES::
+
+        sage: from sage.lfunctions.pari import lfun_hgm, LFunction
+        sage: from sage.modular.hypergeometric_motive import HypergeometricData as Hyp
+        sage: H = Hyp(gamma_list=([3,-1,-1,-1]))
+        sage: L = LFunction(lfun_hgm(H, 1/5))
+        sage: L(3)
+        0.901925346034773
+    """
+    H = pari.hgminit(*motif.alpha_beta())
+    lf = pari.lfunhgm(H, t)
+    return pari.lfuncreate(lf)
+
+
 def lfun_elliptic_curve(E):
     """
     Create the L-function of an elliptic curve.
diff --git a/src/sage/modular/hypergeometric_motive.py b/src/sage/modular/hypergeometric_motive.py
index 8dbec096831..c11bebdadd6 100644
--- a/src/sage/modular/hypergeometric_motive.py
+++ b/src/sage/modular/hypergeometric_motive.py
@@ -982,6 +982,30 @@ def has_symmetry_at_one(self):
         beta_twist = self.twist()._beta
         return self.degree() % 2 == 0 and self._alpha == beta_twist
 
+    def lfunction(self, t, prec=53):
+        """
+        Return the L-function of ``self``.
+
+        The result is a wrapper around a PARI L-function.
+
+        INPUT:
+
+        - ``prec`` -- precision (default 53)
+
+        EXAMPLES::
+
+            sage: from sage.modular.hypergeometric_motive import HypergeometricData as Hyp
+            sage: H = Hyp(cyclotomic=([3],[4]))
+            sage: L = H.lfunction(1/64); L
+            PARI L-function associated to Hypergeometric data for [1/3, 2/3] and [1/4, 3/4]
+            sage: L(4)
+            0.997734256321692
+        """
+        from sage.lfunctions.pari import lfun_hgm, LFunction
+        Z = LFunction(lfun_hgm(self, t), prec=prec)
+        Z.rename('PARI L-function associated to %s' % self)
+        return Z
+
     def canonical_scheme(self, t=None):
         """
         Return the canonical scheme.