We have to change the proof of Lemma 3 only slightly.
Unfortunately, the notation from number theory slightly conflicts with the notation from probability theory.
Slightly refining a result of [8], Davenport proved ......
The estimates (5) then follow by slightly increasing the value of $m$.
They are all slightly different.
Note that (2) is a slightly weakened version of the Pólya inequality.
The motivation for the results of this section is the following result of John (paraphrased slightly to suit our purposes).
Go to the list of words starting with: a
b
c
d
e
f
g
h
i
j
k
l
m
n
o
p
q
r
s
t
u
v
w
y
z