Affiliation:
1. Mathematics Department , 6756 Brigham Young University , Provo , UT 84602 , USA
2. Mathematics Department , 14589 University of Illinois at Urbana-Champaign , Urbana , IL 61801 , USA
Abstract
Abstract
Let L be an even lattice of odd rank with discriminant group
L
′
/
L
{L^{\prime}/L}
, and let
α
,
β
∈
L
′
/
L
{\alpha,\beta\in L^{\prime}/L}
.
We prove the Weil bound for the Kloosterman sums
S
α
,
β
(
m
,
n
,
c
)
{S_{\alpha,\beta}(m,n,c)}
of half-integral weight for the Weil Representation attached to L.
We obtain this bound by proving an identity that relates a divisor sum of Kloosterman sums to a sparse exponential sum.
This identity generalizes Kohnen’s identity for plus space Kloosterman sums with the theta multiplier system.
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