diff --git a/pandas-stubs/_typing.pyi b/pandas-stubs/_typing.pyi
index baa358a8a..7ec2fe200 100644
--- a/pandas-stubs/_typing.pyi
+++ b/pandas-stubs/_typing.pyi
@@ -568,6 +568,8 @@ S2 = TypeVar(
     | BaseOffset,
 )
 
+SN = TypeVar("SN", bound=bool | int | float | complex)
+
 IndexingInt: TypeAlias = (
     int | np.int_ | np.integer | np.unsignedinteger | np.signedinteger | np.int8
 )
diff --git a/pandas-stubs/core/series.pyi b/pandas-stubs/core/series.pyi
index 209237746..13a657d8d 100644
--- a/pandas-stubs/core/series.pyi
+++ b/pandas-stubs/core/series.pyi
@@ -94,6 +94,7 @@ from pandas._libs.tslibs.nattype import NaTType
 from pandas._typing import (
     S1,
     S2,
+    SN,
     AggFuncTypeBase,
     AggFuncTypeDictFrame,
     AggFuncTypeSeriesToFrame,
@@ -916,10 +917,16 @@ class Series(IndexOpsMixin[S1], NDFrame):
     @overload
     def map(
         self,
-        arg: Callable[[S1], S2 | NAType] | Mapping[S1, S2] | Series[S2],
+        arg: Callable[[SN], S2 | NAType] | Mapping[SN, S2] | Series[S2],
         na_action: Literal["ignore"] = ...,
     ) -> Series[S2]: ...
     @overload
+    def map(
+        self,
+        arg: Callable[[S1], S2 | NAType] | Mapping[S1, S2] | Series[S2],
+        na_action: Literal["ignore"],
+    ) -> Series[S2]: ...
+    @overload
     def map(
         self,
         arg: Callable[[S1 | NAType], S2 | NAType] | Mapping[S1, S2] | Series[S2],
diff --git a/tests/test_series.py b/tests/test_series.py
index 9c99dba41..306910323 100644
--- a/tests/test_series.py
+++ b/tests/test_series.py
@@ -3276,6 +3276,7 @@ def test_map_na() -> None:
 
     mapping = {1: "a", 2: "b", 3: "c"}
     check(assert_type(s.map(mapping, na_action=None), "pd.Series[str]"), pd.Series, str)
+    check(assert_type(s.map(mapping), "pd.Series[str]"), pd.Series, str)
 
     def callable(x: int | NAType) -> str | NAType:
         if isinstance(x, int):
@@ -3285,9 +3286,45 @@ def callable(x: int | NAType) -> str | NAType:
     check(
         assert_type(s.map(callable, na_action=None), "pd.Series[str]"), pd.Series, str
     )
+    check(assert_type(s.map(callable), "pd.Series[str]"), pd.Series, str)
 
     series = pd.Series(["a", "b", "c"])
     check(assert_type(s.map(series, na_action=None), "pd.Series[str]"), pd.Series, str)
+    check(assert_type(s.map(series), "pd.Series[str]"), pd.Series, str)
+
+    s2: pd.Series[float] = pd.Series([1.0, pd.NA, 3.0])
+
+    def callable2(x: float) -> float:
+        return x + 1
+
+    check(
+        assert_type(s2.map(callable2, na_action="ignore"), "pd.Series[float]"),
+        pd.Series,
+        float,
+    )
+    check(
+        assert_type(s2.map(callable2), "pd.Series[float]"),
+        pd.Series,
+        float,
+    )
+    if TYPE_CHECKING_INVALID_USAGE:
+        s2.map(callable2, na_action=None)  # type: ignore[arg-type] # pyright: ignore[reportCallIssue, reportArgumentType]
+
+    s3: pd.Series[str] = pd.Series(["A", pd.NA, "C"])
+
+    def callable3(x: str) -> str:
+        return x.lower()
+
+    check(
+        assert_type(s3.map(callable3, na_action="ignore"), "pd.Series[str]"),
+        pd.Series,
+        str,
+    )
+    if TYPE_CHECKING_INVALID_USAGE:
+        s3.map(
+            callable3, na_action=None  # type: ignore[arg-type] # pyright: ignore[reportCallIssue, reportArgumentType]
+        )
+        s3.map(callable3)  # type: ignore[type-var] # pyright: ignore[reportCallIssue, reportArgumentType]
 
 
 def test_case_when() -> None: