AbstractIn this article, we prove an Omega result for the
Hecke eigenvalues {\lambda_{F}(n)} of Maass forms F
which are Hecke eigenforms in the space of Siegel
modular forms of weight k, genus two for
the Siegel modular group {Sp_{2}({\mathbb{Z}})}.
In particular, we prove\lambda_{F}(n)=\Omega\biggl{(}n^{k-1}\exp\biggl{(}c\frac{\sqrt{\log n}}{\log%
\log n}\biggr{)}\biggr{)},when {c>0} is an absolute constant.
This improves the earlier result\lambda_{F}(n)=\Omega\biggl{(}n^{k-1}\biggl{(}\frac{\sqrt{\log n}}{\log\log n}%
\biggr{)}\biggr{)}of Das and the third author. We also show that
for any {n\geq 3}, one has\lambda_{F}(n)\leq n^{k-1}\exp\biggl{(}c_{1}\sqrt{\frac{\log n}{\log\log n}}%
\biggr{)},where {c_{1}>0} is an absolute constant.
This improves an earlier result of Pitale and Schmidt.
Further, we investigate the limit
points of the sequence
{\{\lambda_{F}(n)/n^{k-1}\}_{n\in{\mathbb{N}}}}
and show that it has infinitely many
limit points. Finally, we show that {\lambda_{F}(n)>0}
for all n, a result proved earlier by
Breulmann by a different technique.
On the Hecke eigenvalues of Maass forms
