Affiliation:
1. Institut für Mathematik , Humboldt-Universität zu Berlin , Rudower Chaussee 25, 12489 Berlin , Germany
Abstract
Abstract
Fresán, Sabbah, and Yu constructed motives
M
n
+
1
k
(
Kl
)
{\mathrm{M}_{n+1}^{k}(\mathrm{Kl})}
over
ℚ
{\mathbb{Q}}
encoding symmetric power moments of Kloosterman sums in n variables. When
n
=
1
{n=1}
, they use the irregular Hodge filtration on the exponential mixed Hodge structure associated with
M
2
k
(
Kl
)
{\mathrm{M}_{2}^{k}(\mathrm{Kl})}
to compute the Hodge numbers of
M
2
k
(
Kl
)
{\mathrm{M}_{2}^{k}(\mathrm{Kl})}
, which turn out to be either 0 or 1. In this article, I explain how to compute the (irregular) Hodge numbers of
M
n
+
1
k
(
Kl
)
{\mathrm{M}_{n+1}^{k}(\mathrm{Kl})}
for
n
=
2
{n=2}
or for general values of n such that
gcd
(
k
,
n
+
1
)
=
1
{\gcd(k,n+1)=1}
. I will also discuss related motives attached to Airy moments constructed by Sabbah and Yu. In particular, the computation shows that there are Hodge numbers bigger than 1 in most cases.
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