Littlewood polynomials are polynomials with each of their coefficients in the set
{
−
1
,
1
}
\{-1,1\}
. We compute asymptotic formulas for the arithmetic mean values of the Mahler’s measure and the
L
p
L_p
norms of Littlewood polynomials of degree
n
−
1
n-1
. We show that the arithmetic means of the Mahler’s measure and the
L
p
L_p
norms of Littlewood polynomials of degree
n
−
1
n-1
are asymptotically
e
−
γ
/
2
n
e^{-\gamma /2}\sqrt {n}
and
Γ
(
1
+
p
/
2
)
1
/
p
n
\Gamma (1+p/2)^{1/p}\sqrt {n}
, respectively, as
n
n
grows large. Here
γ
\gamma
is Euler’s constant. We also compute asymptotic formulas for the power means
M
α
M_{\alpha }
of the
L
p
L_p
norms of Littlewood polynomials of degree
n
−
1
n-1
for any
p
>
0
p > 0
and
α
>
0
\alpha > 0
. We are able to compute asymptotic formulas for the geometric means of the Mahler’s measure of the “truncated” Littlewood polynomials
f
^
\hat {f}
defined by
f
^
(
z
)
:=
min
{
|
f
(
z
)
|
,
1
/
n
}
\hat {f}(z) := \min \{|f(z)|,1/n\}
associated with Littlewood polynomials
f
f
of degree
n
−
1
n-1
. These “truncated” Littlewood polynomials have the same limiting distribution functions as the Littlewood polynomials. Analogous results for the unimodular polynomials, i.e., with complex coefficients of modulus
1
1
, were proved before. Our results for Littlewood polynomials were expected for a long time but looked beyond reach, as a result of Fielding known for means of unimodular polynomials was not available for means of Littlewood polynomials.