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Kloosterman sums on orthogonal groups
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Abstract
We study Kloosterman sums on the orthogonal groups
$$SO_{3,3}$$
S
O
3
,
3
and
$$SO_{4,2}$$
S
O
4
,
2
, associated to short elements of their respective Weyl groups. An explicit description for these sums is obtained in terms of multi-dimensional exponential sums. These are bounded by a combination of methods from algebraic geometry and p-adic analysis.
Title: Kloosterman sums on orthogonal groups
Description:
Abstract
We study Kloosterman sums on the orthogonal groups
$$SO_{3,3}$$
S
O
3
,
3
and
$$SO_{4,2}$$
S
O
4
,
2
, associated to short elements of their respective Weyl groups.
An explicit description for these sums is obtained in terms of multi-dimensional exponential sums.
These are bounded by a combination of methods from algebraic geometry and p-adic analysis.
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