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Far East Journal of Mathematical Sciences (FJMS)
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Abstract:
u ,
v : F q
®
C
be
any functions. Then we consider the sums
over
w
Î
O – (2n , q )
and
over
w
Î
SO – (2n , q ),
and,
for
char ( F q )
¹
2,
also
the sum
over
w
Î
O – (2n , q ).
We
show that all of them are polynomials in q
with coefficients involving certain simple
sums. In addition, we show that the number of
elements
w
Î
SO – (2n , q )
with
tr
w = b ( b
Î
F q )
is
equidistributed, as b
varies over
F q .
Keywords and phrases: sum, orthogonal group, Bruhat decomposition, maximal parabolic subgroup, equidistribution.
Number of Downloads: 383 | Number of Views: 1013
P-ISSN: 0972-0871
E-ISSN: 2584-1246
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