Hecke operators on theta series attached to lattices of arbitrary rank
Announcement of errors in "The Eichler Commutation Relation for theta series with spherical harmonics" (Acta Arith. 63 (1993), 233-254)
The Eichler Commutation Relation for theta series with spherical harmonics
It is well known that classical theta series which are attached to positive definite rational quadratic forms yield elliptic modular forms, and linear combinations of theta series attached to lattices in a fixed genus can yield both cusp forms and Eisenstein series whose weight is one-half the rank of the quadratic form. In contrast, generalized theta series - those augmented with a spherical harmonic polynomial - will always yield cusp forms whose weight is increased by the degree of the...
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