Abstract
We present the classification of reflective quadratic forms
−p
x
2
0
+
x
2
1
+…+
x
2
n
for
p
prime. We show that for
p=5
, it is reflective for
2≤n≤8
, for
p=7 and 17
it is reflective for
n=2 and 3
, for
p=11
it is reflective for
p=2,3, and 4
, and it is not reflective for higher values of
n
. We also show that it is non-reflective for
n>2
when
p=13,19,and 23
. This completes the classification of these forms with
p
prime.