diff --git a/datafusion/src/physical_plan/expressions/nth_value.rs b/datafusion/src/physical_plan/expressions/nth_value.rs
index 577c19b54ade0..cb03fde3ae914 100644
--- a/datafusion/src/physical_plan/expressions/nth_value.rs
+++ b/datafusion/src/physical_plan/expressions/nth_value.rs
@@ -20,7 +20,7 @@
 use crate::error::{DataFusionError, Result};
 use crate::physical_plan::{window_functions::BuiltInWindowFunctionExpr, PhysicalExpr};
 use crate::scalar::ScalarValue;
-use arrow::array::{new_empty_array, new_null_array, ArrayRef};
+use arrow::array::{new_null_array, ArrayRef};
 use arrow::datatypes::{DataType, Field};
 use std::any::Any;
 use std::sync::Arc;
@@ -127,19 +127,19 @@ impl BuiltInWindowFunctionExpr for NthValue {
                 value.len()
             )));
         }
-        if num_rows == 0 {
-            return Ok(new_empty_array(value.data_type()));
-        }
+        assert!(num_rows > 0, "Impossibly got empty values");
         let index: usize = match self.kind {
             NthValueKind::First => 0,
             NthValueKind::Last => (num_rows as usize) - 1,
             NthValueKind::Nth(n) => (n as usize) - 1,
         };
+
         Ok(if index >= num_rows {
-            new_null_array(value.data_type(), num_rows)
+            let data_type: &DataType = value.data_type();
+            new_null_array(data_type, num_rows)
         } else {
-            let value = ScalarValue::try_from_array(value, index)?;
-            value.to_array_of_size(num_rows)
+            let scalar = ScalarValue::try_from_array(value, num_rows)?;
+            scalar.to_array_of_size(num_rows)
         })
     }
 }
diff --git a/datafusion/src/physical_plan/expressions/row_number.rs b/datafusion/src/physical_plan/expressions/row_number.rs
index 0444ee971f40d..7c4d0324e830c 100644
--- a/datafusion/src/physical_plan/expressions/row_number.rs
+++ b/datafusion/src/physical_plan/expressions/row_number.rs
@@ -59,7 +59,7 @@ impl BuiltInWindowFunctionExpr for RowNumber {
 
     fn evaluate(&self, num_rows: usize, _values: &[ArrayRef]) -> Result<ArrayRef> {
         Ok(Arc::new(UInt64Array::from_iter_values(
-            (1..num_rows + 1).map(|i| i as u64),
+            1..(num_rows as u64) + 1,
         )))
     }
 }
diff --git a/datafusion/src/physical_plan/window_functions.rs b/datafusion/src/physical_plan/window_functions.rs
index 4f56aa7d38262..366f59a3a4054 100644
--- a/datafusion/src/physical_plan/window_functions.rs
+++ b/datafusion/src/physical_plan/window_functions.rs
@@ -20,13 +20,13 @@
 //!
 //! see also https://www.postgresql.org/docs/current/functions-window.html
 
-use crate::arrow::array::ArrayRef;
 use crate::arrow::datatypes::Field;
 use crate::error::{DataFusionError, Result};
 use crate::physical_plan::{
     aggregates, aggregates::AggregateFunction, functions::Signature,
     type_coercion::data_types, PhysicalExpr,
 };
+use arrow::array::ArrayRef;
 use arrow::datatypes::DataType;
 use std::any::Any;
 use std::sync::Arc;
diff --git a/datafusion/src/physical_plan/windows.rs b/datafusion/src/physical_plan/windows.rs
index 2f539057c82f4..a5f23374a53bb 100644
--- a/datafusion/src/physical_plan/windows.rs
+++ b/datafusion/src/physical_plan/windows.rs
@@ -29,6 +29,7 @@ use crate::physical_plan::{
     Accumulator, AggregateExpr, Distribution, ExecutionPlan, Partitioning, PhysicalExpr,
     RecordBatchStream, SendableRecordBatchStream, WindowExpr,
 };
+use crate::scalar::ScalarValue;
 use arrow::compute::concat;
 use arrow::{
     array::ArrayRef,
@@ -42,6 +43,7 @@ use futures::Future;
 use pin_project_lite::pin_project;
 use std::any::Any;
 use std::convert::TryInto;
+use std::iter;
 use std::ops::Range;
 use std::pin::Pin;
 use std::sync::Arc;
@@ -187,11 +189,13 @@ impl WindowExpr for BuiltInWindowExpr {
                     .collect::<Vec<_>>();
                 self.window.evaluate(len, &values)
             })
-            .collect::<Result<Vec<_>>>()?
-            .into_iter()
-            .collect::<Vec<ArrayRef>>();
-        let results = results.iter().map(|i| i.as_ref()).collect::<Vec<_>>();
-        concat(&results).map_err(DataFusionError::ArrowError)
+            .collect::<Result<Vec<_>>>()?;
+        if results.len() == 1 {
+            Ok(results[0].clone())
+        } else {
+            let results = results.iter().map(|i| i.as_ref()).collect::<Vec<_>>();
+            concat(&results).map_err(DataFusionError::ArrowError)
+        }
     }
 }
 
@@ -246,21 +250,25 @@ impl AggregateWindowExpr {
         let values = self.evaluate_args(batch)?;
         let results = partition_points
             .iter()
-            .map(|partition_range| {
+            .map::<Result<_>, _>(|partition_range| {
                 let sort_partition_points =
                     find_ranges_in_range(partition_range, &sort_partition_points);
                 let mut window_accumulators = self.create_accumulator()?;
-                sort_partition_points
+                let result = sort_partition_points
                     .iter()
                     .map(|range| window_accumulators.scan_peers(&values, range))
-                    .collect::<Result<Vec<_>>>()
+                    .collect::<Result<Vec<_>>>()?
+                    .into_iter()
+                    .flatten();
+                ScalarValue::iter_to_array(result)
             })
-            .collect::<Result<Vec<Vec<ArrayRef>>>>()?
-            .into_iter()
-            .flatten()
-            .collect::<Vec<ArrayRef>>();
-        let results = results.iter().map(|i| i.as_ref()).collect::<Vec<_>>();
-        concat(&results).map_err(DataFusionError::ArrowError)
+            .collect::<Result<Vec<_>>>()?;
+        if results.len() == 1 {
+            Ok(results[0].clone())
+        } else {
+            let results = results.iter().map(|i| i.as_ref()).collect::<Vec<_>>();
+            concat(&results).map_err(DataFusionError::ArrowError)
+        }
     }
 
     fn group_based_evaluate(&self, _batch: &RecordBatch) -> Result<ArrayRef> {
@@ -328,7 +336,7 @@ impl AggregateWindowAccumulator {
         &mut self,
         values: &[ArrayRef],
         value_range: &Range<usize>,
-    ) -> Result<ArrayRef> {
+    ) -> Result<impl IntoIterator<Item = ScalarValue>> {
         if value_range.is_empty() {
             return Err(DataFusionError::Internal(
                 "Value range cannot be empty".to_owned(),
@@ -341,7 +349,7 @@ impl AggregateWindowAccumulator {
             .collect::<Vec<_>>();
         self.accumulator.update_batch(&values)?;
         let value = self.accumulator.evaluate()?;
-        Ok(value.to_array_of_size(len))
+        Ok(iter::repeat(value).take(len))
     }
 }