diff --git a/absl/random/distributions_test.cc b/absl/random/distributions_test.cc
index 850796e..4340aeb 100644
--- a/absl/random/distributions_test.cc
+++ b/absl/random/distributions_test.cc
@@ -470,6 +470,13 @@
   EXPECT_NEAR(6.5944, moments.mean, 2000) << moments;
 }
 
+TEST_F(RandomDistributionsTest, ZipfWithZeroMax) {
+  absl::InsecureBitGen gen;
+  for (int i = 0; i < 100; ++i) {
+    EXPECT_EQ(0, absl::Zipf(gen, 0));
+  }
+}
+
 TEST_F(RandomDistributionsTest, Gaussian) {
   std::vector<double> values(kSize);
 
diff --git a/absl/random/zipf_distribution.h b/absl/random/zipf_distribution.h
index 0600cfc..15f03ee 100644
--- a/absl/random/zipf_distribution.h
+++ b/absl/random/zipf_distribution.h
@@ -57,7 +57,7 @@
    public:
     using distribution_type = zipf_distribution;
 
-    // Preconditions: k > 0, v > 0, q > 1
+    // Preconditions: k >= 0, v > 0, q > 1
     // The precondidtions are validated when NDEBUG is not defined via
     // a pair of assert() directives.
     // If NDEBUG is defined and either or both of these parameters take invalid
@@ -152,7 +152,7 @@
     : k_(k), q_(q), v_(v), one_minus_q_(1 - q) {
   assert(q > 1);
   assert(v > 0);
-  assert(k > 0);
+  assert(k >= 0);
   one_minus_q_inv_ = 1 / one_minus_q_;
 
   // Setup for the ZRI algorithm (pg 17 of the paper).