Affiliation:
1. Department of Mathematics Education, Dongguk University WISE Campus , Gyeongju , Republic of Korea
Abstract
Abstract
Let
Q
Q
be an integral positive definite quadratic form of level
N
N
in
2
k
2k
variables. Further, we assume that
(
−
1
)
k
N
{\left(-1)}^{k}N
is a fundamental discriminant. We express the average theta function of
Q
Q
as an explicit sum of Eisenstein series, which are Hecke eigenforms by applying Atkin-Lehner involution.