diff --git a/src/RationalFunctionField.jl b/src/RationalFunctionField.jl
index 9211359798..91baa4307f 100644
--- a/src/RationalFunctionField.jl
+++ b/src/RationalFunctionField.jl
@@ -10,7 +10,7 @@
 #
 ###############################################################################
 
-function rational_function_field(k::Field, s::VarName; cached::Bool=true)
+function rational_function_field(k::Field, s::VarName = :t; cached::Bool=true)
    return Generic.rational_function_field(k, Symbol(s); cached=cached)
 end
 
diff --git a/src/generic/RationalFunctionField.jl b/src/generic/RationalFunctionField.jl
index 0fa5e5e9df..3ec0c8b0f3 100644
--- a/src/generic/RationalFunctionField.jl
+++ b/src/generic/RationalFunctionField.jl
@@ -34,10 +34,6 @@ function is_exact_type(a::Type{S}) where {T <: FieldElement, U <: Union{PolyRing
    return is_exact_type(T)
 end
 
-function characteristic(R::RationalFunctionField)
-   return characteristic(base_ring(R))
-end
-
 ###############################################################################
 #
 #   Constructors
@@ -127,6 +123,12 @@ function deepcopy_internal(a::RationalFunctionFieldElem, dict::IdDict)
    return R(deepcopy_internal(data(a), dict))
 end
 
+function characteristic(R::RationalFunctionField)
+   return characteristic(base_ring(R))
+end
+
+is_finite(R::RationalFunctionField) = false
+
 ###############################################################################
 #
 #   Canonicalisation
diff --git a/test/generic/RationalFunctionField-test.jl b/test/generic/RationalFunctionField-test.jl
index f08a28d060..3680b94995 100644
--- a/test/generic/RationalFunctionField-test.jl
+++ b/test/generic/RationalFunctionField-test.jl
@@ -6,6 +6,7 @@ end
 @testset "Generic.RationalFunctionField.constructors" begin
    # Univariate
 
+   T, x = rational_function_field(QQ)  # verify default variable name is provided
    T, x = rational_function_field(QQ, "x")
 
    @test rational_function_field(QQ, "x", cached = true)[1] === rational_function_field(QQ, "x", cached = true)[1]
@@ -75,6 +76,14 @@ end
    @test isa(12//(y + 2), Generic.RationalFunctionFieldElem)
 
    @test isa(((x + 1)//(y + 2))//((y + 3)//(x + 4)), Generic.RationalFunctionFieldElem)
+
+   T, = rational_function_field(QQ)
+   @test characteristic(T) == 0
+   @test !is_finite(T)
+
+   T, = rational_function_field(GF(3))
+   @test characteristic(T) == 3
+   @test !is_finite(T)
 end
 
 @testset "Generic.RationalFunctionField.printing" begin